[Mithalwen]

That isn't actually the case. We know that the cloaks of the company were woven by Galadriel and her maidens, Rohan has women - there is a camp in the Hold of Dunharrow which houses the exiles from Edoras "women and children and old men". and in Underharrow and Upbourne "where many sad faces of women looked out from dark doors". Bree had children which necessitates women somewhere. Balin's party may have had women but the dwarves by their culture would not advertise it and how could anyone else tell given the nature of Dwarf women.

So yes I find it quite easy to distinguish between places that are ruled by women (Lorien) or have high profile royal women (Rohan and Rivendell) and places that must have had women (Bree) and somewhere from which the women have been evacuated other than those working for the healers (and the only named one basically a figure of ridicule).

Minas Tirith not only has no woman of significance but the last one "withered in the guarded city, as a flower of the seaward vales set upon a barren rock". Minas Tirith has few children, few gardens, the claim of Arvedui was refused because "in Gondor this heritage is reckoned through sons only"