The largest drawback for melee boxing is that follow breaks when melee starts.
Even hunters suffer from this to a degree, as auto shot switches to melee on its own, when a mob is very close.

Any time follow breaks, you need to hit the follow key to start it up again.
If your toon is swinging in melee, it will constantly drop follow until you get out of melee.

Rogues are interesting, as follow will work until you enter combat.
If you vanish successfully, you're out of combat and follow will work again.

The interact with target, combined with click to move, can have a melee toon move towards a chosen hostile.
Have not experimented too much with this, but have seen a few posts here, so it is doable.
A lot of people box paladins or deathknights, which are both all melee teams too, so it is certainly doable.