It isn't intended to be sexist but in general, it is men who tinker with engines for hours alone in a garage. It tends to be men who hide away in man cave sheds at the end of a garden with train collections, never ending ordered trays of accurately measured screws by type and by metal variety. Of course women can love and tinker with technology but the type of obsessive behaviour and sheet love/obsession/infatuation with buggering around with it is mostly done by men. It is why there are giant lopsided numbers of men and women on mechanical degree places at University, why the vast majority of mechanics, plumbers, electricians are male.
I work with Autistic children and 95% of the boys are obsessed with trains and can explain their inner workings to a high level. That starts at a young age, around four or five. It is why Thomas the Tank Engine/Thomas and Friends does gangbusters in the Special Needs sector.
Like I said, I think there are loads of great female candidates for the Doctor, but I think the general population would find those 'man in love with his machine' aspects more unbelievable if the Doctor were female.
I mean, there was a huge outcry at the thought of Jodie Kidd being one of the new Top Gear team. There was less negative reception to Guy Martin's rumoured involvement. Why? Because he is a man, mechanically minded and an out an out petrol head.
Hey, I might be wrong. But I'm only arguing it from a very specific aspect of the Doctors personality. They could totally downplay those aspects and go with something new, but then for a lot of people it may not feel like Doctor Who.