It's not just easy mode, there's stuff you can do with Super Sonic that you can't do with regular Sonic, because he's so fast and also handily invulnerable, he's a very different experience and fun to just mess around with. I'd consider him less "easy mode" and more like the Debug mode, just one more fun thing to play with and add value to the game.
I agree with Zeta on Special Stages. They work better when they're informed by the main game, as evidenced by Street Fighter II versus Mortal Kombat. Sonic 1 (both versions!) did it best, and the Bonus Stages in S3&K work under the same principle.
I can see the appeal of this sort of thing, and it's the same style of bonus round that you'd see in old arcade games, where the core gameplay is re-purposed to do something different, but as a kid, I really appreciated the Sonic 2, CD, and S3K Special Stages more for their extra variety, and in all honestly, the effects were pretty dazzling at the time. A rotating maze is really cool. A full screen 3D tube is really cool. A big ball covered in other balls is... well, I guess it's cool too. (Also consider the bonus round in the arcade Shinobi--far more eye catching to prospective players than the main game.) I can recall distinctly playing Sonic Adventure in a store once and a kid watching asked "what is the rest of the game like? This is just the Special Stage, right?" I don't think the special stages were dropped because they fell out of fashion so much as they would just no longer be those visually impressive bonuses that turned heads, because the games themselves were so much more visually impressive. When they brought it back in Sonic Heroes it certainly wasn't because it was visually impressive or even fun (they were awful), it was to go with the game's nostalgic themes.