They already do this. People select their partner based on similar education levels. And if you get donor eggs or sperm, they almost exclusively take sperm from donors who are taller than 5’10” and who went to an elite school. They include SAT scores on the application, but I don’t think they verify as there was some dude who made all kinds of bogus claims and famously a significant proportion of the kids he fathered have serious mental and emotional problems, similar to him. For donor eggs they charge a premium for women from elite schools and they’re more likely to demand to see what she looks like first and favor pretty donors.