First of all, Sonic is generally built around being the most height handicapped character between the three main protagonists, if not all the playables in general. He's a character focused on horizontal movement, not vertical movement. Giving him a double jump would go against this mentality.
This isn't really a point, it's just restating the issue. The fact that Sonic doesn't have anything to aid in verticality is exactly why there is such a campaign disparity between Sonic and most other characters. Attempting to balance the character with this in mind is exactly what's causing these issues in level design and campaign progression for new players.
For that matter, double jump doesn't intrinsically go against the idea of Sonic moving horizontally. With momentum being preserved, Sonic no longer would rely on the thok to obtain super high speeds -- more importantly, the double jump is excellent at allowing Sonic to cross tight gaps without losing any of that momentum. The focus isn't to make Sonic less fast, but to make him more balanced.
Second of all, a drop dash could be useful for changing directions on a dime like the thok, the difference would be Sonic would have to touch the ground for it to work. This compliments Sonic's speedy, horizontal movement based design.
Third of all, it would compliment momentum preservation on slopes much better to also introduce it with the drop dash, as the drop dash would be much more powerful for Sonic to transfer from one slope ramp to another with, keeping up great speed in the process that the other characters would have a little bit of a harder time with. This point is especially true if the speed of the drop dash depends on how much momentum Sonic is carrying. If the level design absolutely demanded for Sonic to gain vertical height, it would be much more satisfying for him to earn it by launching off a ramp rather than just pressing jump a second time.
A dropdash has all of the same issues I stated for the thok, but it's even worse because it can only be used on the ground.
I'm not seeing how the thok is prevented from preserving momentum on slopes, as Sonic can always spin right after thokking to roll up a slope at high speeds. The supposed exceptionality of the dropdash for this purpose is something I'd need to see a demonstration of.
Finally, it would make the Sonic and Tails combo as well as the wind shield a lot more pointless. Both of these things allow for Sonic to gain extra vertical mobility to reach platforms he couldn't otherwise reach. If Sonic could just double jump up to them anyway, Tails might be viewed as an obsolete partner as waiting for him to be ready to fly the player up would be slow and tedious compared to just jumping up with the double jump. The wind shield likewise would basically just be a pity shield while playing as Sonic.
Sonic and Tails is something I vyed for in order to make it easier for Sonic players to complete the campaign, but it's more of a bandaid than a justification for Sonic's current design. The fact that there's such a giant disparity in the ease of use between S&T and Sonic solo highlights the issues that Sonic has as a character. And giving Sonic a double jump would hardly render Tails "obsolete" in this regard, as there would still be areas that can only be reached by Tails. A double jump allows Sonic to aim higher, but that doesn't make it analogous to flight.
Wind shield is actually very easy to solve: Make it so that the wind shield stacks with the double jump. For that matter, this never came across to me as a serious issue, since the wind shield has always been pretty superfluous for Tails and Knuckles, and even Metal a lot of the time. It's okay for some characters to benefit more from certain shields than others.
If someone absolutely needed to have a double jump, it would probably be more fitting to give it to Tails or Knuckles as an optional alternative move (by pressing spin while jumping) since they are more designed around vertical mobility than Sonic. Sonic champions horizontal mobility instead, by design.
I believe that there is an important distinction between making a character unique and making a character polarizing in nature. I'd like to take this moment to remind everybody that Sonic and Tails (and situationally Fang and Metal) are far and away the dominant speedrunners so far in this patch. Sonic is never used in coop, Tails is overused in coop, and no one
but Sonic is used in match. Knuckles in Tag and H&S is stupid, while Knuckles in time attack is usually just a worse Tails. I don't think I need to remind everybody what happened to Circuit.
At the surface level, it may seem like this is a desirable state of affairs since every character is being used for some specific niche, but what it really does is reduce the meta of each mode to centering around one or two specific characters, leaving the rest forgotten. This is the problem with designing characters in a vacuum and without taking into consideration their relations with other characters, maps, and game modes. It's why a lot of people hate what happened with Knuckles' crouch and why people are constantly asking for mobility options as Amy. Hell, it's one of the reasons to push through preserved momentum physics. I'll be one of the first people to champion playstyle diversity, but I think it would be a mistake to focus solely on this at the expense of game balance.