Sonic games were never purely about speed in the beginning. Sure, you can beat classic Sonic by holding right most of the time, but that's severely breaking down the experience and any game would sound boring at that point.
Sonic had branching paths, not unlike Super Mario World but at the same time, implemented very differently. While SMW rewarded exploration with secret levels, every path in a Sonic level simply leads you to the next level. But what makes this brilliant is the
combination of speed and clever level design, unless you were all the way at the bottom of a stage, falling down wouldn't send you to your death, but just put you on a lower path. Rather than punishing the player for falling via death (immediately, anyway), it just sets you back slightly, dulling one of the major frustrations in every platformer. The rings also exemplify this idea of not punishing the player for failure, you'll lose all of your speed and rings when you get hit, but there's always an opportunity to replenish both. Unlike Mario where you have to find another mushroom while being cautious not to get hit again, with the abundance of rings in Sonic games you can just continue playing without worry, the player isn't immediately punished, it's fun.
Sonic Team was really clever at the time because they completely changed the formula of a platform game while maintaining the fundamentals. Sonic is not overtly different from your standard platformer, with only three things really changing that.
Speed and momentum. Sonic wasn't just fast at first, he either had to get a running start or curl up in a ball and spin out before he could get to top speed. This ties in to what I said previously, everything was designed so that going at max speed was a reward for playing well. Part of the reason 3D Sonic games are so different is the difficulty of pulling these two off in a 3D environment.
Level design. The world itself is what makes Sonic great, you have Mario who goes around using powerups, Mega Man who runs and guns, Sonic who... just proceeds forward at a rapid pace. You can take Sonic out of the equation entirely and the stages of the original Sonic games would still have their identity. A well designed level is what makes going fast fun, and while the original games weren't entirely perfect at this (looking at you, Marble Garden Zone), they did do it the best.
Forgiving the player for mistakes. I already explained it above, but the health system in itself breaks this series away from any other. You don't just die after getting hit, or after depleting a health bar, you basically just get a slap on the wrist and move along on your merry way (unless you're really bad at Sonic games...).
-
TL;DR, Sonic isn't just speed, it's gaining it, maintaining it, and not getting frustrated for dying on that same Goomba every time.