By amazing coincidence, jobs traditionally done by women have traditionally been paid less than jobs done by men.
That's true as a fact. but I think people don't necessarily pay enough attention to the 'chicken and egg' aspect of this. One can equally say that "jobs which were traditionally poorly paid traditionally attracted fewer men than women, since men felt the need to have an income adequate to support a family".
In context, in the 'days of old' we're talking about very few men entered nursing (other than as 'psychiatric nurses' - see below **!), partially because they didn't want it to be assumed that they were gay (!!) but mainly because a nurses' pay was not considered enough 'to support a family
[** 'psychiatric nurses' in those days were quite often ex-prison warders! ! ]
Traditionally, Doctors were mostly men and Nurses mostly women.
Very true. The above offers at least some explanation as to why few men were nurses. As for doctors, it was presumably primarily a question of 'tradition', which meant that few girls would even consider the possibility of training in medicine. Furthermore, in those days relatively few girls had secondary school education (i.e. A-Levels) in relevant (science-related) subjects. I was educated in a single-sex school and when I was in the 6th form, a couple of girls from our 'sister school' had to come to us to do science A-Levels (so they could apply to medical schools) because their schools did not have the required lab facilities (and maybe not even teachers).
Today, however, the GP register, women outnumber men with over 43 thousand female GPs for 35 thousand male GPs. 2021 figures) Out of the 354 thousand registered doctors in the United Kingdom, 186 thousand were men and 168 thousand women
Your figures are a little misleading. Whilst your figures for 'registered doctors in 2021' (354,000 total) are correct, they include a vast number who had retired, emigrated or didn't work for the NHS (but have retained their 'registration'). In November 2022, there were 'just' 132,900 doctors working for the NHS, of which about 47% were female.
...but, yes, there has been a massive change in the gender of doctors. When I started my 'further education' (in 1967) female medical students were quite a novelty (I would guess well under 10%) and they tended to be 'high flyers', since old-school traditional doctors tended to set the bar very high for accepting female applicants!
In dramatic contrast, within a decade or so many medical schools had adopted a policy of trying to have 50% female students. That tended to reverse the previous situation since, at least initially, kt meant they were looking for more female students that there were applicant - so they then had to 'set the bar very low' (academically) for females
The boys still hang on to most of Specialists jobs.
I haven't looked at the figures, but that's not really my current experience. I constantly deal with a lot of 'specialist' doctors, and a very substantial proportion are female. ... and it's not just doctors, the same is true of 'scientists', mathematicians/statisticians and many other disciplines (indeed, including engineers, lorry drivers, airline pilots, fire fighters and many many more)
Having said all that, I'm not quite sure what point you were trying to make
Kind Regards, John