Rocket jumping could be considered a glitch. It was never really designed, it was just an outcome of the physics system in quake. But it stuck, and later on it was added to TF2 (built on a distant descendant of the quake engine) as a central mechanic. Without it, you wouldn't have cool stuff like
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 working on it. I believe the movement mechanics is just a byproduct of simplistic movement calculations.
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.
IMO back then you discovered it either by just playing, or by reading a game magazine. Back then (when Quake II was released), internet guides for games were less streamlined and available. Which was fun for gaming, as you could discover things on your own. It also meant things had to be less min-maxed. Think of a game like World of Warcraft or Diablo when it was just released, they have the very same problem.
We knew, that there is maximum forward and sidespeed but they way they add together is simple vector addition, so you could actually get higher maximum forward speed if you could point that vector forward.
We knew it is possible to preserve momentum when turning in air. We abused this jumping outside of ledges and then turning and going back to where you came from. This was very useful on dm2 where there is a ledge, a pool of laval and a wall that divides the ledge. You are supposed to press a button to actuate a ramp on which you could cross the lava but you could also just jump and turn in air violating any physical intuition. The jump can be seen here https://youtu.be/VT-johLi75w?t=128. This jump has a bunny hop component to it but it is not necessary.
It's fun and it adds depth! Bunnyhopping is easy to learn but hard to master, and (together with related movement mechanics) adds a lot of freedom and dynamism to the game.
Of course, simply adding bunnyhopping to a game built around more realistic movement will drastically change how it plays -- probably for the worse, if the original was well designed. But in the case of Quake it turned out to open up the game in a way that is both superficially fun and competitively interesting. Nowadays the games in the Quake lineage are built around the existence of bunnyhopping and/or strafejumping, and their maps are designed accordingly.
Then you have games that put this front and center, and it looks completely natural, such as Warsow.
Halo CE: backpack reload, double melee, quick camo, etc.
Halo 2: BXR, BXB, RRX, etc.
Halo 5: slide jump, bum jump, boost jump, etc.
Warzone: slide cancel.
But then again, some glitches don’t. Like super-jumping in H2.
That said, walljumps in Mario games started as frame-perfect buggy jumps and later became much easier and reliable.
If you mean the timing of the jump, that's not the case in Quake and its (spiritual and official) successors. You can press the jump key early and hold it until after you land.
(If you mean optimal bunnyhopping is frame-perfect, maybe so, but it's not the kind of mechanic you're expected to master in the sense of performing it optimally; it's more like aiming in FPS games, or most skills in real sports, in that top-level players still vary in their proficiency and even the best are imperfect.)
But instead of going back to read it again you misinterpreted my reply too (thinking I somehow was insisting on the thing you misinterpreted the first time!)
To be clear: all I said was 1) I played FPS’es for as long as they have existed (early 90s) 2) I played CS competitively. These two things are of course separate things and happened about a decade apart.