In the old days, of course, patriarchy paid. Despite tales of fierce female Amazon warriors, sexual division of labor — in which women focused on childbearing and child-rearing while men engaged in war — tended to make societies much more formidable. A nation could lose a large chunk of its fighting-age men and still bounce back, so long as its fertile women remained.
Nowadays, when war isn’t a matter of hacking at people with sharp objects, that matters less. Women’s primary activity is no longer childbearing, and many women will never have kids at all. And even those who do have kids often delay childbearing until their late 20s or even 30s, long after any draft-induced military service would end.
There’s also the question of fairness. In the old days of “patriarchal privilege,” it maybe made sense to require men to put their lives on the line for their nation. But we have equality, now. Women vote, are overrepresented among college graduates, live longer than men, and so on. The last remaining institutional remnants of outdated sex roles are probably the university sex codes that appear to assume that male students are all violent animals, which seems to be the last acceptable gender stereotype.