I agree that support does too much. Not sure about adding another class, I think those 4 are fine we just need a better division of labor. Not sure y they swapped the engineer and medics weapons but I think is safe to say they should swap them back.
Seen medics spend more time laying suppressing fire then reviving. I myself was tempted to shot over reviving. Resupplying is simple enough and since medic should stay near the engagement zone it makes more sense to leave to them and allow assault to breach and engineer to suppress/keep vehicles alive/dead. You can definitely feel it when medics aren't doing their job ( game ends really quick)