I don't think the solution would be to remove healing from Tanks and support from non-Healers, but rather just give healers more things to do. As they keep giving more oGCDs heals and they keep buffing tank self-heals and as bosses damage gets more centered around just tank busters, it effectively gives Healers more downtime to do something other than heal which isn't inherently a bad thing.
But the problem is that they also have to actually have to give Healers something to do with the downtime, the best we currently have is spamming one spell for 27 seconds.