My 12 year old daughter is happy.
My 11 year old daughter is unhappy. It is easy to just decide that anyone against the concept is a middle aged Daily Mail reading sexist, but like most things there are more layers than that..
For my kid and me this is probably our biggest bonding thing, watching Dr who together. She wasn't a particular fan of Capaldi, but she stuck with him, I'm hoping she hangs on for a totally different dynamic before bailing, because before long she is a teenager with no desire to hang out with her dad anyway.
in terms of rating popularity, not just in the UK, but around the world has been dropping steadily, and it's because the new incarnation is, for better or worse, defined by having chemistry between young(ish) Drs and companions. Capaldi threw that off and people bailed. I honestly don't think a female dr, even if you give her an attractive young male companion, is going to create the dynamic that brings audiences back, at least not past an initial curiosity bounce.
***oh and for context, I live in the US and have for 20 years, so the show is more a niche thing, than embedded into popular culture***