Sonic at a fundamental level is an edgy Mario. He is cooler, faster, and he can even become Super Saiyan. It is less that he is based off of a gimmick (of going fast) but that he is gimmicky in nature as competition with Mario. Sonic drinks Mountain Dew while Mario discovers new worlds on mushroom tea. Mario has soul and has a nature of discovery (secrets, new platforms, other worlds). Sonic's world is marked not by discovery but by obstacles that obnoxiously fling you around and impede discovery and control.
I think the perfect sonic game is one that increases your anxiety and frustration tenfold. A game where you are meant to feel an utmost reduced sense of control in a world that flings you around with utter indifference and offers no genuine sense of reward. Sonic is like a homeless person on some kind of amphetamine as he stumbles to hold onto any shiny object or sense of value. A perfect Sonic game would be like Grand Theft Auto except you move at such a high velocity you are always nearing impending doom (from killing yourself by throttling your body into a pit of fucking spikes) and you have to keep on robbing and pilfering to hold onto life as long as possible. A perfect Sonic game would not try to be Mario but would except itself as the failure and neurotic that he is at his core, and push those qualities to create a game of genuine interest. One where you are always so near to the edge and the pressure of retrieving a coin--JUST ONE COIN--to maintain your pitiful existence is maddening enough to keep you on the edge of your seat (this might be accurate to Sega as a commercial endeavor, as well, and why he is so fucking gimmicky). A perfect Sonic game would be to create a platformer that is not the mushroom induced Zen discovery of a Mario game but the desperate and defeating existence of a heroine addict just trying to hold on. He has been in an identity crises for too long because people want to force him into the Mario mold while retaining him as not-Mario. Well, Sonic isn't Mario. Mario is beautiful while Sonic is a fucking gimmicky deadbeat with no essential artistic nature. But that doesn't mean we couldn't make a game where he gets anal raped looking for coins in an alleyway, or something like that (I'm not alone in thinking that would be a perfect Sonic game, right?)