People who are newer typically complain about it, and it makes me sick at times.
This is the specific reason why STJr want to replace it. While not every new player is going to have issues with it, the majority of new players are having issues with it, and this is seen as a problem since they want Sonic to be the most approachable starter character since it's his name on the title screen. Many new players are going to want to pick him first, and they don't want them to feel punished for doing so.
It's not a brainless ability, it works so well with the level design of SRB2.
While I agree with the first half of your sentence, the reason why I agree with it is also the reason why I don't entirely agree with the second half of your sentence. Thok is a move that works better for people who can use it more skillfully. Despite its simplicity, there's a lot of nuance to the ability that skilled players can use to their advantage, and it's great when applied this way. Unfortunately, the experience most new players are having with it is attempting to use it as a platform aid and cannoning themselves into bottomless pits instead, or bouncing off shield enemies... Into bottomless pits instead. Interactions similar to this become all too common in many new players first playthroughs, and the lesson they learn from it is not to use the thok because it gets them into trouble more than it helps them.
If you spam the Thok, that's on you. Stop complaining to others that you don't understand how the Thok works. You quite literally are complaining to change something because you can't handle it.
You outline the problem here and don't seem to realize it. I already summed this up in my previous paragraph. In short though, the issue is that while the thok has a really high skill ceiling, it also unfortunately has a skill floor that is too high for many new players.
As for veterans of SRB2, WHY!? Why would you want to erase such an important part of this fangame's legacy? I wanna hear from some vets about their reasoning, because they baffle me more than a newcomer does.
As a veteran myself, I can't speak for others as personally I don't want to see the thok gone either. However, while I do have an attachment to it being Sonic's ability, the bigger priority to me is that the thok remains a part of the vanilla experience in some form. I generally agree with STJr's sentiment that Sonic should be the baseline that the game is designed around and be approachable to newcomers. If Sonic's ability getting replaced makes the game overall better, then I don't take strong issue with that. It's an overall positive. I just don't want thok gone entirely. Give it to another character like Metal Sonic or make it into a shield ability so that anyone can use it.
I don't think it's a good idea to make the game easier for players who just felt like playing the main character of the game despite the game stating how Sonic is quite difficult to play as in his damn description.
That's a problem with the description, not with the players, which is probably why that description tidbit was removed. Sonic shouldn't be difficult, he should be balanced. He should be the baseline, default experience the level design is built around. Ideally this would mean they'd design the levels to play better and more safely with thok, but a swap to a different ability isn't such a terrible way of going about it either. The goal is to not gatekeep playing as the main character behind a skill floor that is too high for most new players.
It's the player's fault for not taking "...but he finds getting through hazards the most difficult." and "The Speed Thok can be quite hard to control..." seriously.
Even if these lines were still in the game, once again all this does is gatekeep playing as the title character behind a skill floor. This is the kind of warning that should exist for characters that aren't meant to be the first thing the player experiences. First impressions matter a lot, and having your title character warning you not to use them is already getting off on the wrong foot.
Not to mention the fact the new ability will take away the simplicity of the other vanilla characters. While I don't know for sure if it uses a button other than the jump key, it still looks too advanced in either scenario to work well next to the other characters.
The "Breakfast Sandwich" as many have taken to calling it was scrapped some time ago. While I'm not aware of STJr's reasoning behind scrapping it, I can only assume that they agreed with the sentiment that it was unintuitive and overly complicated and in general conflicted with their goal of making Sonic more approachable to newcomers.
I think a good idea for fixing Sonic's verticality issue is to just encourage players to use speed and slopes to their advantage.
I don't think Sonic has a verticality issue, I'd incline more towards saying a large portion of the level design itself has a verticality issue that advantages characters who can gain height more easily. Lots of "climbing" type areas in which the only generally safe option for going fast is upward vertical movement. I do however agree with your main point here, the level design should absolutely be designed to encourage players to gain speed on slopes and use that speed to perform launches.
To be clear though, I don't think uphill level design is bad, I just think that SRB2 overuses it. There absolutely should be sections of the levels designed to slow Sonic down, though I'd prefer the number of these pathways that are mandatory be kept to a minimum. The exhilaration of Sonic gameplay comes from getting into a "flow" state, and suddenly having to slow down and do more careful platforming gets in the way. Yes, the classic games had a tendency of tossing such sections into the levels too, and I'm not a huge fan of it there either. I'm especially not a fan of it getting overused in SRB2 because given the 3D space level designers have to work with, there's no reason to railroad the player into pathways that are going to kill their flow state so frequently.