Hmm, I thought of another possibility. You regenerate health, but only to a certain maximum figure. Getting injured lowers your maximum health, e.g. max health = average of 100% health and the lowest your health has gone since you've had a medkit. A medkit brings actual and max health back to 100%. If you let yourself get beaten to near death you either need to complete the level with only 50% max health, or find a medkit. Consequences, but not too bad. Thoughts?
Just Cause 2 has a health system similar to this. Getting hit a couple times is just a "flesh wound" and heals back after a couple seconds of not being hit. Getting hit more than a certain amount before regeneration occurs will lower the point that the flesh wounds will regenetate to. Stationary 'health cabinets' would fill you back to 100%. Typically there is only one health cabinet per military outpost, so you're encouraged to occasionally use cover, but allowed to fight like rambo if you want.
The regeneration point is clamped to a minimum of about 25% of your maximum possible health, so if you're in a really tight pinch, you're forced into cover fighting, but aren't necessarily doomed.
It seemed to work pretty well, I have no major complaints about that system.