Sacred Haven of Debauchery

So, they realized they needed a female Doctor, but it was not just late, it was disastrously late.

I agree. I'm not very familiar with the classic series, but the idea seems more than adequate; they could have implemented it earlier instead of awkwardly tying it to current trends. It's a shame they chose the second path.
To be honest, I think the next period of the Doctor's decline is not far off, lasting for some years, until the next reboot in more peaceful times.