Why doesn't AC equipment come with dehumidifier only option?
The coil on a good dehumidifier is SIGNIFICANTLY colder than the coil on a typical air conditioner.

A typical central AC unit is configured so the air coming off the coil is approximately 20 degrees (F) colder than the air entering the coil, and tends to be somewhere in the neighborhood of 52-55 degrees (F).

As the air passes over the coil, water below the coil temperature's dew point condenses onto the coil and drips off into the drain pan. When 52F air at 100% RH warms to 72F, its humidity falls to 50%. If it rises to 80F, its humidity falls to 38%.

HOWEVER... if your goal is 72F air that's drier than 50%, or 80F air that's drier than 38%, you need a colder coil. To get 72F air down to 30%RH (or get 80F air down to 23%), the coil temperature needs to be ~39F.

(For more info, Google 'psychrometric chart')

This is why cheap dehumidifiers throw off a lot of heat, but still can't seem to get the room much below 50% RH... and why most typical central AC systems feel clammy at temperatures below 74F. As the temperature falls, they become incapable of wringing enough humidity out of the air to make it feel dry. 

This is also why most window air conditioners leave the room feeling humid at ANY temperature... they just don't get cold enough to properly dehumidify the air, especially at colder temperatures.

This also reveals a nifty hack you can do with some central AC units to radically improve their humidity-removal (at the expense of significantly higher power consumption, and a possible risk of freezing the coil if you aren't careful). If you slow down the air moving over the coil (by reducing the speed of the blower fan), the coil gets colder, and more humidity gets removed from the air.

If your central AC has an "ECM" type motor, read its service manual carefully... especially the part about low-voltage/control wiring. There's an EXCELLENT possibility that it has a jumper/DIP switch/terminal (probably marked "Dh", "DEHU", or "Dehumidistat") that's normally closed, but when open will reduce the blower speed to ~80% of normal. By removing the jumper and opening the contacts, you can get the humidity a good 5-10% lower that you'd otherwise be able to achieve.

On SOME systems, particularly Carrier/Bryant with "PerfectHumidity", there's another option... if you close "red" to "yellow" (powering up the condenser) while leaving green (blower fan) open, it'll reduce the blower speed to 60% of normal. Normally, this mode only gets unlocked if you buy their expensive custom thermostat... but it's fun to play with if you're aware of its limitations. Namely, in that mode, your system will probably run 100% of the time for hours and hours whenever the temperature gets much above 90F. Latent-heat removal is nice, but when it's REALLY hot outside, sometimes you have to sacrifice a bit of latent-heat removal for brute-force sensible-heat removal. You're also at extreme risk of having the coils eventually ice up after a few hours of running like this... the coil gets so cold, and the air is so humid, eventually the condensate starts to freeze in place on the coils before it even has TIME to bead up and drip off into the pan.

I believe Thermostats like Ecobee and Nest support the 80%-vs-100% mode on systems that are capable of it, but AFAIK, only Carrier's proprietary thermostats properly use "Super-Dehumidify" mode.

Aside from being able to achieve extreme dehumidification, the reduced-speed modes serve another purpose: they allow you to extend your running time on days when it's humid, but not particularly hot. This is where Carrier's "Super Dehumidify" mode REALLY shines... on a cold February day when it's 62F outside, rainy, the AC hasn't cycled on for more than a few minutes at a time all day (because it's technically 72 inside), and the humidity is becoming oppressive, 20 minutes per hour in S-D mode can work miracles for dehumidifying your house.

Just to add an additional disclaimer, there's another factor to consider when attempting extreme dehumidification using central AC alone. Modern evaporator coils (the part that cools the air as it passes through it) have significantly denser cooling fins than old units did, which combines with the surface tension of water to leave the coil a lot "wetter" than they used to be on older systems. If your system is programmed for maximum energy-efficiency &amp; keeps the blower running for 90 seconds after turning off the compressor (the EnergyStar-mandated default), half the water that was pulled out of the air by the coils is going to get evaporated right back into the house. To prevent it, search your air conditioner's service manual. If you're lucky, there will be jumper settings on the circuit board (or in the installer menu, if you're using a proprietary communicating-type thermostat) to delay turning on the blower fan until a few seconds AFTER the compressor starts and the coils become cold, and to eliminate (or at least, reduce to something like 5-10 seconds) the delay before the the blower turns off after shutting off the compressor.

The phenomenon of having the coil freeze during extended run cycles is well known, and is the reason why heat pumps have an explicit 'defrost' mode. Grossly oversimplifying, a heat pump heats a house by air-conditioning the outside and dumping the waste heat inside. Running a heat pump (in heating mode) for hours and hours at a time when it's already cold &amp; humid outside is basically the same situation as running an air conditioner at low blower speed with cold, humid air for hours and hours at a time. The difference is, with heat pumps, it's expected to happen, and they're designed to mitigate it. Most home air conditioners AREN'T designed to deal with running a supercold evaporator with slow, humid air for hours and hours at a time, so they'll ice up if you aren't careful. My advice: if you're making your own thermostat and decide to run the blower at reduced speed, have it kick the speed up from 60% to 80% after 15-20 minutes, and have it kick the speed up to 100% after 40-60 minutes. The algorithm can definitely be improved upon, but this simple logic will generally be good enough to prevent coil-freezing if the system is working properly.

Also, note that contrary to marketing propaganda, a dual-stage compressor will NOT necessarily give you better EXTREME-humidity-removal than running a conventional single-stage compressor with the blower at reduced speed. As noted, latent heat removal uses a LOT of energy... if your goal is 72F @ 32% or less, running the compressor at low-speed might not actually get (or keep) the coil cold enough to SUSTAIN that kind of intense humidity-removal. If your system won't allow you to reduce the blower speed enough when the compressor is running at low speed to get the coil below 40F, you might very well find yourself having to run the compressor at regular speed and just cycle off the compressor and blower the same way you would with a single-stage system to achieve extreme dehumidification.

In any case, achieving extreme dehumidification with a central AC alone almost always requires the use of a homebrew thermostat and controller (Arduino, RasPi, ESP8266/ESP32, etc) and a lot of tweaking, because it's basically the HVAC equivalent of overclocking a PC. It works... but you're officially on your own, as far as the manufacturer is concerned. And your electric bill WILL reflect your extreme dehumidification habit. Operating your AC at 80% normal blower speed will probably increase your summer electric bill by at least 25-50% compared to what it would be if you endured the higher humidity. On the other hand, it's REALLY nice to enjoy a 72F 28% anti-sauna when it's 96F and 95% outside. ;-)

Also... to answer the original question, some manufacturers DO have add-on modules to dehumidify without cooling. For example, Lennox has a module that sits between the evaporator coil and air duct &amp; can be switched in to use the waste heat from the evaporator coils warm the air after cooling it when operating in "dehumidification" mode. In a climate where your house would often be colder than 70 degrees even if you turned the AC off and left the windows closed, it might be worthwhile. In a climate like South Florida, it's probably unnecessary, and simply reducing the blower speed to 40-60% normal and running for 15-20 minutes per hour would probably be good enough to dehumidify without significantly overcooling the house.

Update: there's another potential snag... condensation on or inside the ducts and/or register grilles. The problem is that when you're relying exclusively on cooling to dehumidity, the dew point of the air in your house will NEVER be lower than the temperature of the coldest air coming off the evaporator coil. So... you're pumping extra-cold air into your ducts, which (depending upon how much insulation you have) will eventually become as cold as the air flowing through them (though if you have good insulation and no leaks, might take a few hours of continuous running to happen). Meanwhile, the air elsewhere in your house has steadily become warmer and picked up moisture from people breathing, coming in when you open a door, etc, so its dew point will be warmer than the air coming from the coil. 

This is a major reason why COMMERCIAL HVAC units "reheat" the air by a few degrees before sending it into the ductwork... to ensure that the air in the ducts is "always" at least a degree or two warmer than the dew point of the air surrounding the ducts. You don't necessarily have to heat the air a LOT... even a degree or two of reheat might be enough to banish 99.8% of sweating ductwork if your average duty cycle is below 60% (ie, if an average cycle consists of 20-30 minutes of running, followed by 20-30 minutes of resting). 

The main thing is, if you end up with sweating ducts, try to avoid allowing the temperature to swing by more than a degree or two between cycles. The greater the swing, the longer the subsequent cooling cycle will be. The longer a cooling cycle runs, the colder the surface of the duct will eventually become, and the greater the likelihood that it will become cold enough for condensation to form.

If only the register grilles "sweat", you MIGHT be able to mitigate the problem by replacing metal grilles with plastic ones (ideally, with a hydrophilic coating)... the plastic won't get quite as cold, the coating will cause any condensate that forms to form a molecule-thick film spread over the surface instead of beading up, and hopefully that thin film of water will evaporate away quickly once the cycle ends and before the next one begins.

To some extent, ALL ducts carrying non-reheated air are going to sweat at least a tiny bit occasionally (say, for a few hours when recooling the house after something like a hurricane prevents the system from running for a few days). Good insulation can prevent most of it, but it's still a good idea to try and locate the ductwork someplace where rare drips of condensate can evaporate quickly without damage. Put another way, try to have something BESIDES drywall directly below the ducts (like Hardiebacker). It's a case where "a difference in quantity becomes a difference in kind". 

Put another way, don't expose yourself to single points of failure. Seal and insulate your ducts well... but don't delude yourself into thinking it's going to completely eliminate the condensation problem. It won't. There's just no getting around the reality that ambient air whose dew point is higher than the temperature of cold air in the ducts WILL result in condensation someplace where warmer humid air comes into contact with a colder surface. 

You can mitigate it actively, by warming the air slightly before blowing it into the ducts and/or dehumidifying it independently of the air conditioner, or if the amount of condensation is very minimal, you might be able to mitigate it adequately by just ensuring that when it happens, it'll drip someplace where it won't cause harm.

Also,  take this as a cautionary tale if you're fantasizing about redoing your home's ductwork using exposed spiral duct to give it a loftlike ambiance. Spiral ductwork requires flawless sealing, excellent insulation,  plastic grilles, AND some form of reheat or additional dehumidification to completely eliminate visible  sweating... especially if those ducts are ANYWHERE near a door leading outside, a bathroom, and/or a kitchen... or if the interior isn't well-sealed and insulated from humid outdoor air.