Women have lived longer than men throughout most of history and in basically every society, so your theory doesn't hold. Childbirth was dangerous but men's work was even more dangerous.
https://pubmed.ncbi.nlm.nih.gov/10902048/
This paper seems to disagree heavily with you.
And extrapolating this to the middle ages and earlier:
In general, countries with a lower overall life expectancy had a lower number of women per 100 men aged 75+, while countries with higher overall life expectancy had a higher female to male ratio in this age group. A hundred years ago there were nearly equal numbers of women and men aged 75+ in many countries.
It doesn't seem to disagree with me at all.
It feels like you're right, but what "feels right" turns out to be wrong pretty often.