One of the quotes I gave included "Before modern day nursing, men were nurses, not women". The files.eric.ed.gov link says "Prior to the organization of female nursing schools and as early as the fourth and fifth centuries, men provided nursing care to members of various religious orders (Cook-Krieg, 2011, p. 22-23), and held the predominant role in organized nursing in western society."

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.