To be honest, it was always gonna be difficult for anyone to replace Piper.
Unlike previous companions, Piper had been sort of the glue of the show as she was the only constant of the first two series.

I the past, companions might have worked with different Doctors, but the Doctor was always the focal point of the show, which of course he still is now, but as the original run was a lot of years, it was very easy to phase one companion out and replace them with another.
As the new Doctor Who had a huge gap in its schedule from the original run, they didnt have the comfort zone of the show being long running, and the fact that (excluding McGann) no Doctor has ever lasted as short a time as Eccleston, they kinda put a lot of emphasis on Rose.
I mean how many shows from the first two series revolved around her, her life and her family?