Rawnsley is reporting on This Week now, maybe he could take over The Politics Show on BBC ONE.
Was he presenting in their "guest reporter of the week" slot? If so I wouldn't suggest it means anything more than he is presenting in their guest reporter of the week slot...
The reverse logic is that Andrew Neil seems to always crop up on the ITV Election Night programme despite being the BBC's chief political presenter really considering he hosts This Week and The Daily Politics.
I know Krishnan Guru Murphy has done that slot on This Week before, which I guess is designed for those outside the BBC.
I think realistically branding a programme "political" inevitably puts off a large chunk of the audience, but the issues discussed if presented correctly could attract a larger audience by branding the programme around the "issues" rather than the "politics" - but that of course would lead to accusations of dumbing down of course.