I have played FPS games for as long as they have existed, competitively in the early days of CS. I don’t see why adding this feature deliberately would be appealing. It makes the game look unnatural for what? There are tons of hard to use glitches in every FPS game and the policy on any enjoyable server is “no glitching”, that is - play the game as the developer intended or be kicked. This bug was just too widely use…
At least in Quake this was not deliberate choice. It was fortunate accident. It took some time for people to discover bunny hopping and once somebody figured it out it took like a storm. Hopping wasn't discovered immediately. I remember we were doing things like strafing into walls to speed up movement before we knew bunny hops are possible. I don't think idSoftware predicted how the game would be used when they were…
What's amusing is you could always tell the keyboard players back then, by the way they slowly turned around.
Anyway, playing with the mouse was a new thing. Mouse acceleration, dpi, etc. were all just experiments. Introducing a new way to move would surely uncover bugs hidden in the physics code that simply weren't possible to hit with keyboard movement.