I know it sounds wrong, but when has any franchise (game or otherwise) ever gotten better when trying to appeal to, and pander to, as many fans as possible? Especially those that are fragmented. I'm honestly trying to think of examples and nothing comes to mind.
Sonic Team should just focus on what made Sonic good and enjoyable. Rise of Lyric was a classic example of using sales figures and focus groups to create a game, SEGA of America wanted Heroes 2 because it sold so well, and fans wanted several playable characters. Look what we got.
Look at Star Wars. It is incredibly fragmented with OT fans, Prequel fans, TCW fans, Rebels fans, fans of the old novels, fans of the gritty video games, fans of the comics. There is no way to appeal to everybody, and the best Star Wars stuff as of recent looks to the stuff that works for inspiration for how to move forward. That is why The Force Awakens borrows so heavily from the OT and Rebels borrows so heavily from The Clone Wars. Sure fans of the old canon are miffed, but end of the day Lucasfilm is focusing on making something of quality. And it worked for them, as nearly every fan of Star Wars (not some subsect) enjoy the new stuff.
I'd also argue that if you claim to be a Sonic fan and do not like the Genesis originals, you are not a Sonic fan. If SEGA were to look to the classics for inspiration in making the 25th anniversary game and you aren't happy with it, you should reassess if you are a fan. Having done the fan site thing for 8 years, I've encountered some pretty zany people who think Shadow as a character and Sonic 06 as a game are great. If a new Sonic thing doesn't feature Shadow or doesn't have a dark gritty story, they're put off. These are not Sonic fans, these are Shadow fans or Sonic 06 fans. There is nothing wrong with this, but they need to understand that they are fans of a small portion of a much larger franchise.