Imagine how a platformer from that time used to be experienced: every single attempt at a playthrough consisted in replaying the entire game from start to finish or, if the player was still unable to beat the game, to the hardest point that could be reached before losing all lives and continues. Each attempt at completing the game pushed the finish line further away until the game was done.
A very serious problem with this classic platforming structure is the piling up at every replay of those "beaten and frankly pointless" in-between levels. Replaying those early levels feels like a chore, and soon it turn joyful platforming into a dull repetition exercise. Now, in 2017 level 1-1 of Mario is considered a masterpiece in player learning, but my child self who replayed it a billion times in the '80-'90 while dealing with 8-1 to 8-4 knew it as something different: a fucking chore where I would farm coins/lives to allow me to stay longer in the levels I actually cared about. Mario dropped the ball on this problem by making players just skip most levels thanks to cheats, but imagine if a game had something that could give value to those old mastered levels, something that gave an added value to remembering paths and flawless repetition.
In Sonic, the player's memory of levels and the ability to execute the same set of jumps again and again turns that platforming dead weight into visual spectacle, with the added benefit of allowing the player to fast track the beaten path as he focuses on the real challenge. And the best part is that the player does not notice it happening: that's the genius idea behind momentum based platforming. The player doesn't need to break a level with an exploit or a hard coded cheat, nor to learn a new set of tools or crazy skills that allows him to go faster and do things he could not before: he will naturally redo his actions with less mistakes, and less mistakes will make his momentum not drop, which will make his playthrough naturally faster. Not only that, but this extra speed will naturally lead to some new passages that were too hard or just ignored the first time around. The way I played Green Hill Act 2 the day i got the game was radically different from week 1, and completely different from month 1.
However while speed is great and gives a reason to revisit and enjoy old content... Isn't it all a visual trick and a slight convenience? But we want real gameplay! Not gimmicks! I mean, the player is STILL replaying the same levels and redoing the same thing again and again until it becomes routine, right? If only the game had something that forced the player to go out of their comfort zone, forced them to question if their choice of path made in the very first playthough was the best choice... something like a premium currency, a currency tied to speed in some way...
Rings as health items are to Mario's mushrooms what Halo's regenerating health was to Half Life, it turns a rigid clockwork system into a lax sandbox that doesn't feel like castrating the player for mistakes, in fact, getting hit is its own procedural minigame that leads to some really amazing moments (My last ring!). How rings are tied to speed? The first playthrough the player will inevitably rely on monitors to get the easiest fix of rings required to get a life or enter a bonus stage, however players who are enjoying the replay of the first levels as speedrunners will naturally tend to shift their focus from still targets to "ring clouds" along their chosen path. Finding ring clouds and the best rings/speed ratio paths is the main motivator into experimenting in old beaten levels: after all, you still need to pile up lives for the more challenging parts and get to those bonus stages.
Summing it up, that's how Sonic works:
Day 1 - It's a normal platformer, and if you don't believe it, they put spikes everywhere to remind you.
Day 3 - It's a normal platformer where you start to get fast in the earlier part without noticing.
Day 7 - You noticed how fast it can be, now you tend to re-optimize the early level paths and wonder what you've been missing. You've also likely beaten the pure platformer playthough, most platformers of that time would be DONE right now.
...
Day 30 - You are super sonic.