I don’t think a Who house would ever happen in the current administration of the BBC. They’re notorious for “staying on their island” when it comes to picking licensors and making deals; all their T-shirts are made by British companies, all their toys, all their video games, etc.
This is the company that told Joe Hill, Stephen King’s son who had Neil Gaiman adjust his pitches, “we have never let an American write for Doctor Who, and if we did, we wouldn’t start with you.”