> The term nosocomial originates from the latin nosocomi, the name given to male care-givers, meaning that men were prominent in Ancient Rome
... If they needed a special word for male care-givers in ancient rome, that implies they assumed care givers were female by default.
I don't see how you can therefore infer that men weren't the majority of nurses back then.
As for the term "nosocomi", it doesn't imply that care givers were female by default. Latin is a gendered language. A different word would have been applied to female caregivers. As an example from Spanish, think "maestro" and "maestra" for male and female teacher, respectively.
If the Latin only used the masculine form, and never the feminine, then it indicates the job was primarily (or perhaps only) done by men.
Consider the word "maid", short for "maiden" meaning "female virgin." We have a special word for female domestic workers but that doesn't imply that domestic workers were male by default.
Similary, in many English speaking parts of the world, a senior or supervisory nurse is a "sister". This title includes males, eg. from https://www.researchgate.net/publication/282839878_Clinical_... "… what was nice there was a senior male sister that welcomed us and orientated us, so that really help me a lot to accept the situation …".
A male sister may also be referred to using the gender neutral term "charge nurse".
Again you see that a gendered term for a given job does not imply that job is usually done by the other gender.
Or, we have "mailman", "chairman", "cabin boy" for jobs which were usually done by males, while "charwoman", "lunch lady", and "call girl" indicate females. The existence of a special gendered term doesn't mean the mail was usually delivered by women, or that prostitutes were usually men.
Your understanding isn't correct, at least for nursing.
Nurses were male until the 1800s. https://en.wikipedia.org/wiki/Men_in_nursing#History give examples of predominately nurses and caregivers in other cultures before that time. http://minoritynurse.com/rethinking-gender-stereotypes-in-nu... says "Before modern day nursing, men were nurses, not women. The earliest recorded nursing school was established in India around 250 B.C. It was exclusively for men; women were not allowed to attend because it was believed that women were not as pure as men."
What happened in the 1800s? Quoting from https://files.eric.ed.gov/fulltext/EJ1081399.pdf :
> Through the efforts of Florence Nightingale in the mid-nineteenth century, nursing was established as a women's profession (Hus, Chen & Lou, 2010). Nightingale's image of the nurse as subordinate, nurturing, domestic, humble, and self-sacrificing, as well as not too educated, became prevalent in society. The American Nursing Association ostracized men from nursing until 1930, when as a "result of a bylaw amendment, provision was made for male nurses to become members of the American Nurses' Association" (In Review - American Nurses' Association, p. 6). Looking back in nursing history, Florence Nightingale, and the American Nursing Association ostracized men from the nursing profession.'
See also http://onlinelibrary.wiley.com/doi/10.1046/j.1365-2648.1997.... , "History appears to indicate that men have had a place in nursing for as long as records are available, but their contribution has been perceived as negligible, largely because of the dominant influence that the 19th century female nursing movement has had on the occupation's historical ideology."