You definitely identified the issue with people hogging medic but man these changes would suck, running across map is already a hell of a boring task and this just makes that more of a pain in the ass. Keeping the frontline action going is a big part of the fun, and this slows the game down in a terrible way, not the tactical way.
I think your medic changes are kinda okay, maybe just do half health or 1/3 instead of the normal 1/4 because killing someone only to get them rezed to nearly full is pretty frustating. As china said, a lot of people like to choose medic just for the uptime, so giving assault classes some way to heal while not being op would be a potential solution, as it diverts some attention away from medic as a class. We could have it so the bandages also heal but I think it might be better to limit it to only reviving, and have it be a gadget instead. A stim or whatever works, the point is that it would limit the offensive power/utility of the person while in exchange granting uptime in combat. Maybe to avoid making it free healing it can be a temporary recovery of health, idk.
As for nade spam? Not sure, I just deal with it using buildables and smokes
Honestly, as a medic main the points are incentive enough but I can see why some just care more for the healing. Maybe a cooldown or recharge delay for self healing, that way if you stay out of combat like a medic should, you aren't really affected as much.
Really, being active as a medic is probably the turnoff for most people, they forget they can toss a medkit onto the ground, and their teammates don't even notice it being there to heal from it. People aren't gonna be a medic if they wanna play a traditional shooter, it's just hard to get players to switch to being a medic no matter what game. Making it so less people hog medic is about the best that I can cook up atm.
Extending the drag range to make revives safer would be nice, I feel that should be done to make it more common