I was bothered by that too, since her character and backstory with Tony was very similar to Sunset Bain's backstory with Tony. We already had a "first love of Tony's when he was a teen who used him and who grew up to be a crime boss". What need was there to introduce a new one? Sunset was already there.
I guess the silver lining to it is that he didn't end up messing up Sunset in any way since he left her alone. When Bendis is on his game he can do some really good work -- but when he's off, he can really screw up a character's voice, personality, etc.
Her being a pop star was part of the appeal, as I recall. It gave her a legitimate excuse to do all sorts of world travelling, and as a celebrity she would potentially have access to other "important people", etc. Basically a 'hide in plain sight' situation, exploiting her celebrity status.