It's actually quite ingenious in its simplicity in how it adapts to players of all levels:
For a beginner player, it allows great flexibility in taking hits and surviving to the end of the stage. A beginner just wants to get to the next act and is not necessarily concerned with getting a high ring count or score. As long as they have at least 1 ring, they can achieve this.
An intermediate player will start appreciating semi-high ring counts and begin to play more carefully in order to keep them, forcing them to learn stage layouts, find more efficient paths or more rewarding item boxes. While losing them all suddenly feels bad (I mean shouldn't it?), it's also a moment of learning for the next replay which feels good. Also an intermediate player doesn't need to rack up obscene ring amounts to be rewarded. Lives and access to bonus stages are easily within reach at 50/100 ring milestones. Subsequent playthroughs may also see these players find the locations of helpful items like shields (extra hit, bouncing, attracts more rings), which feels immensely rewarding.
An advanced player, now taking into account all of their experience is encouraged to take the most optimized, rewarding path in the stage for score. Experimentation and exploiting the layouts and natural physics of the stage all build for a highly satisfying, replayable gameplay loop for each stage. The mounting ring count also adds a progressively scaling sense of tension as you near the end of a stage. You want to keep them all. As you replay the stages, you'll come to see which paths grant you the fastest route and most rings by the end.
The key thing with Sonic games is that they all condition the player to replay the stages for better performance as you learn their layouts. The more you dive into their replayability, the more rewarding each playthrough is. It's one of gaming's finest, most unique health mechanics that can be appreciated on several levels, while being so simple both a beginner/child or veteran player can understand and leverage it in different ways on their way to the end of the stage.