> make surplus is a few tens of thousands, way to small to make up an army

...why would you populate your army solely with the surplus? The point is you have a buffer that you can burn without immediately impacting your demographics for the long term.

> that is not the reason why men and not women go to war

It's a serious theory [1]. (It's more correct to say the surplus and it share a common cause.)

[1] https://link.springer.com/rwe/10.1007/978-3-319-19650-3_931