I'd query the idea that Billie was more famous than Eccleston. At the time her claims to fame were A/being the British Britney for a very short period of time and B/being married to Chris Evans (not that one) whereas Eccleston was very well known for things like Cracker, Our Friends in the North etc. You could maybe argue they were equally well known, for different reasons, but no way was Billie more well known then CE. Tennant on the other hand, well when he began she was clearly the better known.
But this comes back to something I said months ago. I can't think of any instance where the a new Doctor's companion was more famous than him, except where it was an existing companion (Sarah Jane with Tom or Rose with David). That said just because it's never been done it doesn't mean it's a bad call. My worry has always been that it potentially sends a message out that the producers lack faith. The first female Doctor and you give her a companion who's an older white male who's also better known than her (in the UK at least).
That said this does seem to be Chibnall's call and it seems like he's gone out of his way to get Walsh, and never wanted anyone else for the role, which is another slap in the face for Jodie (IMO) given she had to bloody audition. Hell even Peter Capaldi had to audition!
None of which will stop me saying Walsh is bloody brilliant if he is in fact bloody brilliant.