In regards to making Sonic the only character able to use shield abilities, I feel that I should point out that the only reason he was the only character that could use them in S3&K is because they actually planned to let him use all 3 abilities regardless of shield or lack thereof, but moved the abilities to the shields to reduce control clutter.
This is the first I'm hearing of this, but even if it's true it doesn't change the fact that in the product we got Sonic is in fact the only character in S3&K that can use the shield abilities, and as such the impact of making Sonic more unique in that game is very real. Even if they had gone with Sonic always having access to the double jump, bounce, and air dash it still would make him stand out from Tails and Knuckles, so nothing really changes in regards to this discussion. If anything, it would make Sonic unfairly unique since he would have several more utilities at his disposal at any given moment than the other characters.
Either way, the general consensus seems to be that Sonic with no ability would be a net negative SRB2 overall, and that a different approach should be taken to solving the thok dilemma. My particular favorite individual ideas personally are giving Sonic parkour, replacing thok with the SA2 bounce attack, and making it so that the thok is a pure momentum redirection tool that scales to your current speed or to regular max running speed if you are moving slower than that.
Parkour would give Sonic more ability to move along and up walls, still giving him the horizontal advantage over Tails and Knuckles while still leaving the vertical advantage to Tails and Knuckles while giving Sonic a little more to work with than before. It would also be helpful for helping Sonic maintain speed, and he would have to earn it to begin with as parkour wouldn't inherently grant him speed.
The Bounce Attack with horizontal momentum preservation would allow Sonic to reach higher platforms than his regular jump can reach after a few bounces, and could be used similarly to the thok in performing badnik/monitor bounce maneuvers, though with a higher emphasis on vertical rather than horizontal launching. This would give Sonic a more reliable utility to reach high up places without outright giving him Knuckles climbing or Tails flying, keeping him unique. Easier access to otherwise Tails only shortcuts would help give speedrunners the sense of speed they are looking for with Sonic.
Momentum adjusted thok would feel like a nerf at first, not giving Sonic any additional speed than just running along the ground. However, should you manage to get moving faster than that, thokking would match your new speed. If you were to lose your speed, you would lose it on thok too, being unable to just instantly get it back. However, Sonic would have a reliable tool to instantly change the horizontal direction of his momentum while moving fast without losing any speed, giving him a powerful ability to make sharp turns while in midair. This would overall help safeguard slower, newer players by not encouraging them to use it as a pure distance tool and fly off cliffs, while skilled veterans moving at high speed through the stages would have a powerful tool to make use of to make some tricky jumps while doing speedrun maneuvers.
I feel like any of these three ideas would be significantly better than simply just not giving Sonic an ability at all.