Arma 3 replaced the jump mechanic with a "climb over obstacle" mechanic, and after so many hours playing that game, I've never encountered any occasion where I thought that that wasn't the right way to handle it.
But on the bigger scale, I think player movement and controls is just a function of what kind of gameplay flow and feel you want.
We've had this discussion recently on the Dark Mod forums, since some people want to greatly speed up the speed of mantling, jumping, sliding, and a few other things, and they posted some videos of many games that used that faster speed side-by-side with the Darkmod version.
My basic opinion was I didn't like it, not because he didn't notice a legitimate difference, but because I thought gameplay is on a spectrum from more simulationist (like Arma 3, where you shouldn't have jumping at all) to more gamey (like recent FPSs where you want mantles and jumps to be inhumanly quick), and each step in either direction is changing the character and flow of your gameplay and the feel of the game in those directions.
I actually tend to think of walking sims (which don't have jumping at all, and are prone to restrict areas you access with invisible walls, etc.) are on a gamey end on the other direction as the FPS-gamey direction, and proper sims are about versimiltude about how humans actually handle space. (There's also a whole discussion about what movement you want the player to directly control vs. some elements you want to externalize to compensate for the lack of environment feedback, things like the screen marking the direction you're being injured, or the lightgem in Darkmod, etc. But that's another related issue.)
So anyway that's the way I think about it. There's no objectively right or wrong answer. Or let me try to phrase it properly. It's a design decision about what kind of character you want for your game, and if you want to capture that character, it'd be best that you design the movement and control elements consistent with the norms for that character.
It sometimes happens though that a designer thinks their game is in one genre, but as the game comes together, sometimes the game itself has a natural tendency towards the genre that best captures what it is, as the designers begin to understand what it is... So I think that's the case when these kind of dynamics come into play, when a designer actually gets it wrong what the character of their own game really is, and over time it becomes more clear and the natural pressures will come into play that push players into wanting those elements to go in the proper direction, e.g., making jumping quicker or getting rid of jumping or whatever it is.
Playtesting often helps tease those things out. But it can happen in the opposite direction too, which is what I thought about that Darkmod criticism case, where there's a demographic out there that really wants to push Darkmod in a gamey FPS direction that IMO is really antithetical to its natural character...
But over time majority opinion of gamers may shift, where twitchy norms or walking sim norms get so set in a certain group of players that they start demanding it even in places where it doesn't belong at all (because, e.g., they just haven't been exposed to the history & sensibility of different genres), which is actually a little concerning to me. I want to see different gameplay sensibilities continue to be represented and respected, and I don't want to see certain pop norms dominate to the extent that they suffocate off certain sensibilities just because it doesn't mean anything to them in their limited experience.
That's the kind of things I think about in this neighborhood.
Edit: Okay, I'll be explicit with some examples.
- You need jumping in Darkmod because environment-negotiating gameplay is core gameplay (although as environment negotiation, not jumping puzzles per se).
- I can tolerate the quick mantles and jumps in post-Dishonored immSim FPSs, even if they're not to my taste, I recognize its core to the character of that genre, & if I were on the design team I'd demand them too.
- As I said, it'd be wrong to have jumping in Arma3 & it's proper it handles it with the climb-obstacle action.
- As for walking sims & other games inspired by them or building out of that root... that will take a whole other post, because I'm not gungho about this trend of cinematicizing games and want gameplay to still be a core part, but even then I recognize if you want a walking sim or cinematic flow, you want to make sure you don't have jumping, etc, to respect or capture that character.
I think you could gather my probable thoughts on other examples from that.