Ahah!!
Well, i have some experience with this, seeing as how in my homebrew, there are no gods and no clerics.
Druids, Bards, and Paladins take their place for healing. As it turns out, it doesn't really suffer for it.
Not allowing Druids does make it worse, but not so bad. Bards cast spontaneously, so they don't have to study only healing. They just have to pick a healing spell up here and there.
Undead Turning is used by Paladins or not at all. It doesn't make the undead more powerful, but it does add a small consideration when dealing with such creatures.
I wouldn't allow the "arcane" casters healing magics. In my setting, Bardic magic isn't really arcane, so it keeps a line drawn between the spell casting classes.