I like the idea of medic rules.. I've been to games that have used different variations.
The problem with them is that the more complex they are, the more likely players will completely ignore or abuse them. Brian pretty much has it right from what I've seen.
I think the best variation I played with was a disengagement rule. When you're hit, a "medic" has to tend to you (usually a simple tag). You then go to the closest of several marked "forward spawn" places where you went to respawn after the first hit (put a red sash around your arm after this hit). If your hit again and wearing a red sash, you have to go all the way back to the main spawn.
It was simple enough to follow and provided the best balance of having medics vs. getting players back into the action.
If you wanted to force players to make better use of medics, you need a real, quantifiable team penalty for respawning instead of using a medic. But then comes the aforementioned problems of complicated rules, players ignoring them, etc. etc.
"Someone in a Prius tried to race me at a stop sign the other day. I couldn't believe it. I had him for the first 100 feet or so but I can only walk so fast."