Tony Vargas
Legend
Yes, you may goad monsters into Overkill and 'waste' their damage or 'gain' let's-pretend-healing damage due to heal-from-0.That's a small part of it, but not the major portion. Even if cure wounds healed for double its current amount, you still wouldn't cast it until the target was near death. It's just more efficient that way.
Sure, bloodied, even without disadvantage, did that for most characters - monsters could be more dangerous when you were bloodied, for instance, without having to actually gimp you into some kind of death spiral.The best way to get people to want to heal is to penalize being injured. Maybe bring back the 4e bloodied condition at half HP,and have bloodied targets attack with disadvantage. (That might be too harsh, so you could adjust the threshold to a third or a quarter if you wanted.)
But, I don't think penalties are necessary: just getting rid of heal-from-0, just counting the negative hps, alone would do it, because the 'bonus' is gone.
Of course, a lot of casters would let their dropped allies sit there and bleed rather than waste a decent-level spell, anyway...