100% agree. Having only four classes isn't enough in my opinion, 5 or 6 would make more sense. Of course I'm biased because I grew up on old school Battlefield titles, first and foremost Battlefield 2 which I played for upwards of 2500 hours. The game had 7 classes, which was a bit too much because the Engineer and Special Forces in particular were a little lackluster.
Seperating the medic from the resupply and machine gun role would be ideal in my opinion. Medics could get carbines as their signature class of weapon, being slightly less powerful than assault rifles but still perfectly combat ready.
I do realize though that this won't be changed this late into the development of the game. The decision of something as fundamental to the game design as the class system was made a long time ago, perhaps even well before Battlefield Labs started.