Agree to disagree... respectfully.
The problem primarily isn't that Sonic having more upward verticality would make other characters redundant (though it somewhat would), it's that other characters already provide ample upward verticality, so giving it to Sonic is totally unnecessary and redundant and takes away from the entire point to him.
Sonic's uniqueness comes from his lack of needing upward verticality as a double jump ability, and such upward verticality only serves to slow him down. Going uphill is always going to be slower than going downhill, and excessive verticality primarily serves the purpose of skipping level design rather than enhancing it. This is why Sonic is generally designed in the official titles as the default experience, with everyone else being alternative playstyles more designed for players who have either already beaten the game or don't care about experiencing the levels properly.
Also, as I've already explained several times now, Sonic does have upwards verticality, he just has to work for it a little harder than everyone else. Simply pressing jump twice isn't going to give it to him, nor should it.
I never said "Sonic is uniquely horizontal", I said he has to earn his verticality. Wall jumping is exclusively something that Modern Sonic has and generally exists as a more fun replacement for and equivalent to platforming sections that would otherwise just have Sonic jumping up several platforms slowly or riding up a slowly moving platform. Both methods of gaining height serve the same purpose of slowing the player down, and often come just before another section that provides the opportunity to go fast. Generally speaking, when Sonic is truly given the opportunity to gain some height, it requires him to have built up some speed first to make use of in achieving it.
The title character being the default experience is good game design. SRB2's stages are divided into two types of pathway; the main path and side paths. That's not changing, nor does it have any reason to change. Sonic's pathway being designed as the main pathway that most of the other characters can also follow if they choose to is a big chunk of the reason why the levels are fun. Sonic's role in the game is to provide a baseline experience that actually has to interact with the level design as intended to progress on a first time playthrough, while everyone else is given tools in their moveset they can use to simply skip sections of the level design through their boosted verticality. If you give every single character tools to easily skip the level design, your platforming game quickly starts to defeat its own purpose.
That's not to say that Sonic doesn't or shouldn't also have tools to skip. Again, it's simply more difficult for him. His moveset requires skill to perform skips, instead of simply pressing jump twice. He's easy to play, hard to master. This low skill floor high skill ceiling playstyle is what makes Sonic simultaneously accessible and engaging. By giving him unnecessary verticality, you risk trivializing the very thing that should be tricky and precise and lowering the skill ceiling in the process. Worse, you risk compromising the very thing that makes Sonic games fun to begin with, which is the rush you get from earning your speed. Worse still, to focus too heavily on upward verticality is to stray dangerously close to needing slow, tedious, uphill level design that doesn't give Sonic an opportunity to go fast just to make it harder to skip the level design to begin with. You will notice this with the other character exclusive pathways; they are not designed around speed, but rather around mobility. Now imagine that but it's the entire game.
That's not to say that SRB2 needs to be completely restrained by what the mainline series is, but if changes are going to be made to the formula they should be made for good reason and take care not to conflict with what makes it a Sonic game to begin with. If the whole point starts to become to not be like other Sonic games and to get away from them, you're not only going to alienate many of the longtime players but are going to get to the point where you might as well reskin everything to be original instead of being a Sonic fangame, and I honestly doubt that doing so is even remotely STJR's intention.
Agree to disagree... respectfully.