That's where you go off the rails.
A girl from an impoverished background, whose only fault is that she is not a mom, has far more need of "publicly backed financial support" of her education than an upper middle class mom. Publicly backed financial support should be either restricted based on need for everyone, or it should be unrestricted and given to everyone as a matter of course. But telling a girl that she has to have a child before she gets access to this particular pot of money sets up the same restrictive environment and lack of "choice" that you decry in the "evil patriarchy".