Although primogeniture has been discriminatory for basically the entire time it's existed, the discrimination isn't inherent. It's an implementation detail. Modern British Royal succession now uses absolute, gender-neutral primogeniture since 2013.

In fact, there are few things less discriminatory than a random birth order. You may as well be assigned a random number at birth, and the lower your number, the more you're paid. In such a system, there's nothing to discriminate against; the ordering is absolute and immutable, and everyone is treated equally.

I agree that it's a bleak idea, but Animats wasn't talking about subjugating women.