Solution: Oakreef's patented hybrid health system that encourages both exploration and pushing forward quicklyTM
You have health bar with segments. Each time you get hit you loose a segment. Around the world are rings/coins/gems/energy/whatever for you to collect. As you collect them it fills up a bar and only when the bar is full do you get health back. The bar starts to deplete if you don't collect anything for a while (slowly at first but accelerates the longer you don't collect) and it fills up more if you collect things faster (i.e. collecting five rings in quick succession fills it up faster than collecting five rings over a period of ten seconds).
When you get hit you keep your current charge but loose a piece of the health bar and also drop a load of rings that you can collect to recharge but you never drop enough to fully recharge the bar, only about half or three quarters. If you get hit a bunch at once you'll drop enough rings to recharge some of that lost health tho.
Side areas you find by exploring can contain big caches of rings to heal with or big rings that instantly fill the charge.