What are the benefits of 700c23 tires?
WIDER TYRES ARE FASTER

Every study on rolling resistance (including ones carried out by the leading tyre manufacturers) demonstrates clearly that wider tyres have LOWER rolling resistance and not just at the same pressure. This is also verified by many people (including myself) who use 25mm-28mm and much wider tyres on a regular basis and will never go back to anything narrower.

For vast majority of road cyclists there isn't a single rational reason (other than time trailing) for using 23mm tyres if the same model is available in 25 or 28 or wider width. On some bad roads (e.g. UK) it's actually unwise and dangerous to bounce around on such narrow piece of rubber.

There are several reasons why the myth of "fast" narrow tyres is still alive and kicking.


23mm is everywhere from the adverts, your local bike shop, cycling club to the TdF.
It's inconceivable for most of people to think that so many people around them could get it so wrong. Most of folks just go with the flow and don't ask questions. 
People believe that they can "feel" rolling resistance and if narrow tyres are pumped up to its usual 100-120PSI it feels fast. You can't feel rolling resistance but you have to methodologically measure it with a power meter of some sort. Firmness and discomfort doesn't translate to speed, quite the opposite. 
It's a common belief that rolling resistance is just a function of 
a contact patch and the lower the contact area the faster the tyre is. The facts are that the shape of a contact patch and volume are more important than the total area.
People assume that rolling resistance is just about hysteresis (friction/resistance with the tyre itself) and nothing else. They are unaware of (or ignore) "suspension losses"
which occur on some less than perfectly smooth roads (most) and are about energy lost on lifting the rider/bike on imperfections of the surface. 
For the same reason but on a much larger scale most of experienced mountain bikers with half brain run their tyres at a low pressure to go faster as even small obstacles (even bumpy field or gravel) are absorbed more effectively with less energy lost.
People confuse assumptions and beliefs with hard evidence. How many times you've read/heard: "Surely there is a reason why 23mm tyres are so popular..." "Surely if the pros use 23mm tyres..." Assumptions don't prove anything.
Some people (like one of the posters) have tried wider tyres and they found them slower.
Only comparing identical tyres in different sizes make sense and it's pretty obvious that a 23mm Michelin Pro3 is going to be faster than a 28mm Gatorskin due to a different design. Also the difference in speed that 2-3mm difference offers is most likely very small and can be only measured during repeated tests with a power meter at various pressure levels to find each tyre's sweet spot.
Many people have never tried anything wider as their frames/forks don't have enough clearance and more sensible and practical bikes taking wider tyres aren't "good/fast" enough for them or don't look right. They've never tried any fast wider tyres like Rivendell Jack Browns 33.3333mm or Schwalbe Kojaks 35mm or some fast 650B tyres. They have never run a pair of custom shaven completely bold 26x2.00 Schwalbe Furious Fred 120TPI 3oog mountain bike tyres on the road. It could be an eye opener.
Narrow tyres can be pumped up to higher pressures and higher pressure equals more speed. That's incorrect. As you increase the pressure, rolling resistance is going down but then at a certain point starts climbing sharply due to reduced ability of the tyre to conform to the non-perfect road surface (suspension losses). Even on a track/velodrome you won't benefit from 200PSI.
For every tyre width/volume, road surface and the rider's weight combination there is always an optimal (fastest) pressure. High pressure on its own means absolutely nothing.      
The pros use it! 
This the favourite argument of the defenders of status quo. You can't argue with it, can you?


Well... the pros ride at completely different speeds and therefore the aero benefits are probably more significant than rolling resistance. An average amateur rider would be naive to worry about the air flow differences between 23-28mm tyres. 
Weight is also crucial as winning the stage / future career can be decided on a single climb. Again people worrying about the weight difference of several grams (rotating or not) may be slightly over-anxious. 

The pros used to use 19mm tyres too in the past and now they are very slowly migrating to 25mm tyres. Were they wrong at the time, or are they wrong now or they will be wrong in the future? What if they discover that 28mm is even better? Will everyone be blindly following them? 
The truth is that they are as guilty as you and me of being humans and use stuff that feels right and also aren't immune to peer pressure. 

Road cycling community tends to be very traditional, conservative and protective of the status quo as I've experienced on other forums and in real life but for being open-minded and embracing "new" things can greatly benefit one's cycling.