I think with the way healers work now, and the way they are designed we have little need of a change, atleast not in the direction you propose.
Healing is inherently “unfun” because the mistakes of others fall on you to fix. This is quite evident in pugs, while it gets a bit better in semi-organised/organised groups.
I personally do not feel bored weaving in heals during fistweaving. I do feel though that I would quickly run out of players to play content with if they get fistweaved instead of our enemies.