Why don't people power LED strips in parallel instead of using amplifiers?
Actually, people power RGB LED strips in parallel all the time.  In fact, simply by using an RGB LED strip, you're wiring the LEDs in parallel, as all of those strips are just a bunch of parallel connected RGB LEDs with their own current limiting resistors (which is the important feature that lets them be safely connected this way).   More accurately, they tend to be groups of 3 or 5 LEDs that share a set of current limiting resistors - hence why you can only cut the strips at every 3rd (or whatever the grouping is) LED.  But every cuttable 'unit' is already wired in parallel.  

So what that means is there is no difference electrically to powering however many strips of whatever arbitrary lengths in parallel vs. one giant strip with the same total number of LEDs.  They're already connected in parallel anyway.  

As long as your power supply can handle the load, you can wire LED strips up to it in parallel and it should 'just work'.  

I don't know why exactly you think people don't do this, as in my experience this is done whenever it is warranted. 

I think the main reason you see strips in series and using amplifiers so much is that, often, one of the main aspects of LED strips is the distance being covered.  If you have a 5 meter LED strip, in many cases, one end of the strip is going to be roughly 5 meters away, or somewhat less depending on how they're being used.  If you need to continue this length beyond 5 meters, to do it in parallel, you now have to run 5 meters of extra wiring.  

This could very quickly get out of hand.  You now have to find a way to run all these extra wires, and it might not look very nice, and greatly complicates things vs. just having series connected strips without any wires, except for a short length and a locally positioned power supply for it.  

But if you had 3 5 meter strips that all begin at roughly the same spot, then in that case it would definitely be preferable to wire them in parallel - and as far as I know, people do do this when the setup allows and with great success.  

All of this is strictly in the context of regular, 'dumb' RGB LED strips.  In the case of addressable LED strips, things are different.  Addressable LED strips are powered in parallel, but they have a serial data bus connected such that each LED has an input and an output, and they relay the signal from one LED to the next, almost like a fire bucket brigade, only instead of water, its bits.  

You can still power addressable strips in parallel, but you must connect the third data wire in series to retain full functionality.  Again, this can quickly become a pain due to the extra wiring.  

Alternatively, if you don't mind that each addressable strip will have identical behavior and show exactly the same pattern as the other strips connected in parallel, you can connect the data line in parallel just like the power connections.  If you do this however, you lose any ability to control the strips independently.  They will always mirror the other strips (assuming they are the same length).  

Note: You should observe the same guidelines for cutting LED strips regardless of how they are going to be wired/connected.  Only cut where the strip indicates it can be cut.  This ensures each group of LEDs has current limiting resistors.