It's a Support class, and Medic is only one aspect of it. LMGs or Carbines or SMGs do the job (or LMGs or Carbines in the closed lobby). But I do agree LMG feels like a worse version of other automatic weapons, and that's what I'd target first to improve Support's overall experience.
What would instantly improve LMG weapon class is heavier suppression effect - including a heavy sway known from previous BFs. Alternatively, Support as a class, could've been providing this kind of suppression on all of the weapons he takes.
