Poor men, having no influence or power gets conscripted against their will. Women, being in the middle, are exempted from conscription but can't volunteer. Rich men, being at the top of influence and power, was exempted from conscription and also had the choice to volunteer (usually for officer or other high ranking positions).
No one denies that the small percent that makes up rich men have more influence and power with more freedom to choose during conscription. Men as a group however is both the poor and the rich. If we only look at the top then we ignore an already marginalized and vulnerable part of the population. Those at the bottom.
This is just a wrong analysis. Women didn't get our of conscription as a result of their power and influence. They were exempted from military service because almost all men, across all classes, were opposed to women serving in the military.
And you are wrong that almost all men, across all classes, were opposed to women serving in the military. Armies that are created by rich men at the top looks very different to those created by lower classes, such as resistance movements in Europe during world war 2.
What you're saying is correct, it's just completely irrelevant.