If this game was slower paced and more deliberate, then that'd be a great idea. This is one of those things that sounds like it'd be a no-brainer, but it doesn't really work out in this game.
In Battlefield you tend to get damaged from so many different sources that it's often a matter of kill, get damaged from the exchange, seek cover, wait for the health to revive and then engage again. If you had to bandage up with a limited supply, or wait for a medic to help you out, it'd really take you out of the fight a significant amount of time every time a stray bullet ends up hitting you. It'd be really difficult to build up significant score streaks.
Retreating to a safe area, especially in game modes like Rush is not always possible. There's often not much room to navigate and even a single step outside of cover could get you killed instantly. If I can retreat towards my teammates, I often already do that, as they can cover my escape while I regenerate.
I hate being forced into engagements where I'm not at 100% health, because that tends to reduce the bullets to kill for most weapons to 1 or 2 bullets at best. Getting in a gunfight, where a single pistol shot just flatlines you isn't my idea of fun. If two players duke it out at full health, that's when gun mastery such as aim, recoil control and spread control come into play.
Indeed, it'd increase the value of the medic, not in a way that would encourage teamwork though. Instead I'd just pick it as if it were the assault class, because it's the only class that'd be able to heal themselves over a prolonged period of time. Because it's not always possible to be a lemming and to be near my teammates all the time. At times I need to take risks, get into the enemy flank and pull their attention towards myself, so the rest of the team has an easier time pushing forward.
The only thing I've noticed is that Battlefield 6's auto heal feels pretty **bleep** fast and quite quickly puts you back at maximum health. I'd not be against toning the speed at which you regenerate down a bit. Just to make it a more conscious decision whether you're willing to risk taking damage.
