We already have classes like assault etc. but in my opinion it would be nice to give some love to troopers.
They could have special perks that would act as subclass, for example:
We don’t need medics because one of troopers can carry more medpacks. But it would be nice if we could send private Ivan to training and give him perk to increase his skills as a squad medic. Now such perks are random and everybody can have them. I porpose a system that would give us more control over our soldier’s carier. Also, unlike in current system, it could limit number of those perks (one medic subclass per squad for example).
It would also allow to add “classes” witouth adding classes. Like for example MG assistant gunner. (Now I’ll talk about hipothetical situation of MG on bipod.)
We don’t need new class for that but it would give nice, more authentic feeling to the game and may also provide bonuses (like faster reload or faster barrel change), give more ammo (currently it’s just one mag) or even replace dead MG gunner for short period of time (untill you unbipod for example, or just time limited).
I would also add UI indication of the soldier’s subclass in the battle. Sth like small cross in corner for medic etc.
Of course it would require some balancing so it’s not abused. Assistant gunner may have additional barrels for change in he’s second weapon slot (so slot is locked basically), medic may have -1 inventory slot etc.
Also I would make it unlockable via grind. Example: you can choose subclass when soldier has 2 grey stars and it will be unlocked after he reaches 1st golden star. After that he can change class but he will again need to grind to unlock it and he will “forget” about he’s previous skill.
This system would give some meaning to troopers’ lives and also allow flexible way to give players more powerful perks (+30% vitality cough cough) with limitation.
It may also be quite cinematic 
(with proper animations that is).
