In general, I feel that Sonic games should strive to make their controls as simple as possible. Sonic 1 was intentionally built around one-button gameplay, and IIRC that'd ballooned to something like seven as of Generations. I'll concede an extra button for the extra dimension, but beyond that you start running into some really superfluous functions.
It comes down to how you wish to design your game. The momentum based design of the original Sonic games fits the 1 button thing to a tee, as you simply have one control for vertical movement and one for horizontal movement. The depth comes from the fact that Sonic speeds up gradually based on how long you hold down the button, as well as slopes and such. Removing additional controls places the focus onto that aspect, giving the level designers a clear way to make the levels.
Sonic advance 2 was brought up earlier, and Azure Dream made a good point about how the game was presented and designed around the 'run
run RUN aspect. It's not a good game due to a couple of crippling flaws (dimps level design), but on a conceptual level it's actually a very important part of the series history, because it's arguably the first game to change Sonic's focus from a traditional platformer with a momentum twist, to being about speed. In other words, Advance 2 is the origin of the boost design, and considering how that kinda saved the series to an extent, it's a big deal.
Consider how speed was handled in SA2 and how it taught Sonic team for the future. It largely uses the 1 button formula, with some extra tricks that aren't hugely essential other than for speedrunners. In particular, I'd like to bring attention to the fact that horizontal movement is still controlled by the d-pad only. Sonic still gains momentum in the old way, but with much more acceleration. When hurtling at such high speeds, this becomes a detriment rather than a boon as it was previously, as you have much less immediate control over your speed, resulting in not being able to react to incoming hazards. The only control is the spindash, which requires you to be standing still. SA2 is frankly frustrating to play as a result. When Sonic team revisited the idea of going super fast, you can see they learned, as Sonic Rush gives you normal running and then boost to control you speed on the fly more easily. Also, they addressed the 'oncoming hazards' issue by making you invincible during boost. The level design is still poor in several cases unfortunately, so it seems like every department (fast music, after images etc) designed around the new philosophy except the level designers. Oops.
I'm going to elaborate on some other things now I'm here as well, I suppose. SA2 is a GBA title as we know, which means a small screen. This is the other fatal flaw of the game imo. Sonic simply takes up too much screen real estate than is possible with that kind of game. They tried to make the camera shift so he's on the far left at high speed, bu it isn't enough. Compare
this, particularly how large Sonic is on the screen, to how
Ubisoft handled it in Rayman Origins. Rayman is tiny on the screen in comparison to Sonic, which is crucial for the high speed chest sections as it gives players time to react. The fact that the chest does it exactly how you are meant to is beating players over the head with visual clues for upcoming challenges, something Sonic entirely lacks (it's a bit of a series wide problem, actually).
The 3D games fit this design much more naturally, as the perspective gives you a better idea of what's ahead by it's very nature. The level designers also seem more competent now at the type of terrain required, with a focus on wider spaces, particularly in Generations.
Going back to the control point, I think even with these elements that have been added to accommodate the speed since SA2, the old reliance on Analog input (well, not actually analog, but in the sense that how long you hold the button is important) is not plausible at such high speeds. The precision required is too punishing. So instead the new controls are all digital inputs. A here to hop, B here to crouch etc. And that requires more than one button to be interesting.
I haven't looked at Sonic Boom or Lost World in any detail, so I can't comment on them.
Also, I haven't posted here in a while, hey people.
