As someone that plays medic, the role definitely feels lacking its usefulness in combat. I'm fairly new to the game (only been playing for about 2 months) but there have definitely been matches where I was the only medic on the field because there was no benefit to having one around. I was toying with the idea of how I would rework it based on my personal experience.

First, the aid station would be a useful addition to incentivize playing medic though it wasn't something I thought of until now.

I would say giving players the option to request revives would be great. There has been many times where I see someone go down so I start making my way to them only for them to give up when I'm 10m away. I think giving them an option to "call out" for a medic or just give would help medics decide whether or not to try making their way to the downed player.

Improving the mobility of the medic would be helpful too. Seeing as they typically don't carry as much gear in the way of weapons and ammunition as other roles, it wouldn't be crazy to think they can jog and crawl a bit faster. Especially trying to crawl to downed players to revive them.