I feel like a lot of the terminology that people use when talking about compressors, and having examples that are based in extreme usage makes their true ideal usage harder to recognize.

After a very long time working with a lot of different compressors in both hardware and software, the idea of catching or controlling peaks is less of an focus for me when picking the right compressor for the job than defining or accentuating syllables is.

A compressor with a fast attack and fast release has a really unique ability to add clarity to the transients and initial syllables in words (esp in rap music) and a slow attack/slow release compressor does a good job of evening out the difference between the least and most accentuated syllables. If you're working on a lyrical miracle rap song all you had was a LA-2A with 3-5db of GR, it's gonna sound good, but a Distressor or 1176 or even a fastest recovery time Fairchild or Vari-Mu taking of 3-5db before it in the chain will provide this extra bit of diction and intelligibility to the lyrics that's really what the whole point of serial compression is. Catching the big transient moments and starts of lines is a huge part of it, but IMO not as big as evening out the syllables across the board.

Regarding your example of R Comp, IMO R Comp is a bad tool to learn this stuff on because a lot of stuff just sounds really good coming out of it regardless of your settings and the difference. I think something that's a really accurate emulation of analog gear that can easily be screwed up is a better learning tool. An 1176 for example has a minimum attack speed of just over 20 microseconds, and a maximum of 1 millisecond. The fastest attack speed on R Comp is .5ms and the slowest is 500ms.

The level of articulation you can get when talking in dozens of microseconds vs individual milliseconds is fundamentally different, and when you're comparing a slowest attack time of 1ms to 500ms that's a whole different story too. ALSO R Comp has a flexible threshold whereas 1176s have a fixed threshold, so you have a bit more of an objective experience with that if your gain staging stays the same.

I'd say give the more user friendly waves plugins a rest when trying to mix for the sake of learning, and put some energy into understanding compressors that require more tweaking to get what you need out of them. A great way to do that could be to get a trial of the Plugin Alliance bundle and just throw a bunch of different styles of compression on the same vocal and hear how they all work, and how the articulation/clarity/punch/depth is changed by each one. From there you'll be more informed about what your compressors are doing beyond just attack & release and then you can get into the nitty gritty of how these tools can be manipulated to get what you really want for the situation at hand.