Interesting video, I don't necessarily agree with all his points but definitely well thought out.
Sometimes I wonder if even SEGA ever truly understood what exactly was the secret sauce in those original games.
If I was going to do it I would literally take a hatchet to everything, throw out the rings, the loop de loops, the ramps, the running tubes, the bottomless pits, the checkpoints, the monitors, the springs, the act system and their end of level banners, the entire supporting cast of characters, literally everything except the main character and his nemesis...
There's only really three essential ingredients that need to be in it to make it a Sonic game, the acrobatic speed, the psychedelic environments, and the killer robots.
Everything else is all just baggage.
Like the guy mentioned in the video, taking out the boosters would actually force the developers to add to the core game play. It's a really simple but valid argument.
If you take out the springs, then you'd have to create a game that can handle high speed twitch parkour in 3d, or how do you get to the top of those buildings. If you don't have ramps and loops and other cliches, you have to make a game where you can wall run and grind almost anywhere you like, and with that the player has actually gained abilities rather than lost them. Take out the pits, and you have to actually consider why Sonic shouldn't just run around at 700mph, maybe it actually hurts when he slams face first into something.
Take out the rings and you have to give Sonic something else to compulsively collect, so what if it becomes a game where you have to pretty much constantly fill up on donuts and hot dogs in order to keep that insane metabolic rate going. You race through every area jumping from street food cart to ice cream stand clearing out whatever isn't nailed down, but it's kind of not stealing... its... er... requisitioning, because you need that energy to fight the real bad guy :)
Then the progression. Throw out the act 1/2/Boss formula and just make it open ended. It starts with Eggman taking over the world. He has giant robots and animal enslavement factories and chemical plants scattered around everywhere. You know the drill. Go whatever direction you want, head straight to the endgame if you feel like it, or go around the world undermining his power and collecting stuff that makes you stronger. Maybe one way gives you the best ending but is incredibly challenging, maybe the way where you bide your time gives you an easier endgame but a least decisive victory... but there is actually something to think about while you are playing, rather than just "hold forward.... now jump"
And then of course the best thing about throwing out all the other characters, the developers wouldn't be able to use them to control the story narrative, and it could unfold before the player much like Half Life rather than being narrated by insipid cutscenes... maybe Tails could get one token line where he says something like "Oh no sonic, Dr Eggman is back and he's destroying everything with his robots" and Sonic says 'Yeah no shit dude, I have eyes you know". Then he gets abducted and is never seen again, and Sonic is like 'Noooooooo! that's the last thing I ever said to him' and becomes all broken and broody like Max Payne.
Every contrived feature you remove from Sonic forces you to replace it with something more sophisticated and interesting to get the same effect. You just have to kill the whole damn series with fire before you can really rethink it :)