Certainly there is no way to compare Billy Pipers pop career to that of Justin Bieber. Maybe someone like Aaron Cater would be closer. A few hits years before but nothing you can really remember. By the time she got this gig she was only remembered for being married to Chris Evans who was at that time a huge star in the UK.
Not a fan of Rose (the episode or the character) and the final nail was when in a confidential for the season 4 finale she said she needed to watch her old episodes on DVD in order to see how to play the character. She isn't Marlon Brando. She just needs to hit her mark, say the words and smile. Can't even do that convincingly.
It is ages since I saw one of her episodes and I can't see that changing anytime soon. Hard to think of a real stand-out episode. They are all a bit average and for me a big part of that is the fact that she is in them. My least favorite of the nu-who companions by a mile.