In a FOWLR
set up (in my opinion) aiptasia are for the most part functionally harmless and perform limited filter-feeding from the water column.
It's in the eye of the beholder whether they're an eye sore or not. The public aquarium in my city actually had an aiptasia display tank:
With that said, the existence of aiptasia in reef tank are an absolute bane.
You can keep the aiptasia if you want to but bear this in mind: if you ever decide to leave the hobby, aiptasia colonies among your live rock will make the live rock (from a reef keeper's perspective) worthless.