I think considering a slower regen for when you're not healed would be interesting (or another solution we could come up with). Sometimes you might go on a nice flank and find yourself out of health, often forcing you to play medic if you want to push for those streaks. I play a ton of Overwatch in which there are dedicated healing characters, which is all right because it's an arena shooter with a way smaller map, but I think no regen in such big maps can be problematic.
What are your thoughts? Is there something I might be missing? Any other potential solutions? Let me know!