Could this fan theory help explain why the Doctor has never been a woman?

Well, not necessarily. In fact, regeneration throws up lots of unanswered questions. Why does the Doctor always become a white human male, yet once speculated he could get “two heads” in 2005 episode The Parting of the Ways? Why do some Time Lords change ethnicity or gender (like the General in 2015 finale Hell Bent) but not the Doctor? Why has he never even been a woman?

And what was with this scene in classic Doctor Who episode Destiny of the Daleks where Time Lady Romana (Lalla Ward) “tried on” several regenerations, including an alien, before picking her final form, a face she already knew, while the Doctor looked on in confusion?

It's given some context in the novelisation of the story, below...

The Doctor’s own regenerations had been rather haphazard affairs, usually in response to some kind of crisis, and the bodies he’d acquired had been very much a matter of pot luck.

Romana, on the other hand, seemed to be changing bodies as casually as she might have changed her dress.

Except that the body she’d finished up with was a direct copy of someone else’s. The Doctor frowned, remembering that in a purely academic sense, Romana’s qualifications from the Time Lord Academy were rather higher than his own. No doubt that accounted for her superior control.

This scene was never fully explained in the series, and it adds yet more mysteries. Even if we assume that the human form is basically what Time Lords look like (the series has previously suggested Time Lord physiology inspired humans and not the other way around), how come Romana can look like an alien when no other Time Lord we’ve seen does? Why were Romana’s regenerations different?

Well, according to reddit user alexmcchessers, it’s because not all regenerations are regenerations. You see, in his theory Time Lords were once shapeshifters, with the same technology/inherited abilities that granted them regenerations also allowing them to change and blend on a visual and cellular level into any species (in a similar way to how a TARDIS's chameleon circuit – when it's not broken – is able to make it resemble something from whichever time or place it lands).

As the reddit post goes on to explain: “The 13-regeneration limit doesn't apply to these voluntary transformations, as their lives are not in danger.

Every incarnation of the Doctor so far

“However, it takes a certain degree of skill to perform – skills that were mostly lost to them once they stopped visiting other worlds as often and retreated to Gallifrey. Romana, being something of a swot, is probably in the minority among her generation in that she took the time to learn it.”

So perhaps Romana wasn't exactly regenerating at all, just using some crossover technology – and PERHAPS this interesting idea can be taken even further within the Doctor Who canon. What if this “blending-in” ability (if we assume it to have existed) actually predates regeneration, and the Time Lords’ immortality was simply a side-effect of just wanting to go undercover? Maybe they found that the method of changing their cells completely was a good trick for cheating death, and so they built it into their DNA.

And later, even if the Time Lords DID stop shape-shifting for fun, maybe a certain amount of that control over appearance lives on in regeneration, but only with the proper training. This could explain why Romana could work it into her own physical appearance, Time Lords like The Master and The Corsair (as mentioned in 2011 episode The Doctor's Wife) could become women while The General changed both sex and ethnicity – but why a certain renegade who stole a TARDIS and probably didn’t finish any sort of training is only able to regenerate into reasonably similar types – like that Roman merchant whose face he chose for his current incarnation...