What he does is actually sever their chi paths, not just the connection. he completely destroys the ability to bend.

all healing does is influence the chi paths to heal wounds and injuries and mental damage. this is why katara can never fully heal an injury like hakoda's or tophs feet without immediate attention or spirit water. there are clear limits. Katara may be the best healer but she isn't the god of healing.

(also katara is hardly a bloodbending expert. she has done it twice and we can assume never again)

Amon's damage cannot be reversed by anything but energybending. think of it like a road. chi blockers can put up traffic cones temporarily, what people think amon is doing is putting a whole road block there, permanently. what he's actually doing is destroying the road entirely. we cannot assume that energybending has a way of regenerating those chi paths in a way healing cannot.

Okay cool @Bastion2.0 . That makes a lot more sense. I thought Amon setting up a roadblock, but he destroyed the road.

I always just assumed it was because katara never trained herself to do it outside of the full moon.