Being nipped at, they can get infections and die quicker than from just the nipping.
Angels are just not a good idea in a reef tank unless it is a very big reef tank where the damage might be minimal.
It's just like keeping a clown goby with hard coral. In a small tank, the effects of the clown goby perching in the corals and irritating them has a greater effect in a smaller tank with fewer SPS coral than in a large tank with more colonies and larger colonies.
It sucks but you have to weigh the pros and cons. Do you want an angel or do you want corals? Angels are known to eat soft coral, clam mantles and SPS polyps.
I love angels as well and have tried to keep certain Centropyge angels in my small 75g reef and it just never worked.
Maybe someday when I get my dream tank of 300-500 gallons, I'll try an angel again. God, I would love to have an Emperor but till then, I'll just dream.