Well AST is one of the most varied, non-repetition based healers due to cards rarely making duplicate pulls happen (unless it's Spire > Ewer > Spire pulls, those seem to happen more than they should). That and it doesn't really have the emergency heal factor of the other two healers, so you can't just use Indom/Assize when it gets rough, you have to survive an extra 3 seconds and it's a bit more exciting.

In terms of fun I think AST is high up there when you're getting good cards and generally things are going well. I think it's the least fun when people are being idiots, or if there's no one worthy of your cards which means you really shouldn't be there in the first place efficiency wise.