Although I don't think state universities should be single-sex, there is a case for allowing men's and women's colleges (Wellesley, Mt. Holyoke, etc.) to exist.
This as a tough question.
Persoanlly, I'd prefer to see all college/uni admissions based solely on merit. To truly institute a system like this, we'd have to base admissions solely on the results of a national exam that would be akin to A levels or the Irish Leaving Cert. Students pick their subjects, spend 3 or more years studying them, and take the test. They get points for their scores, and the universities set minimum points for admission into a subject area. Essays, letters of recommendation, extracurriculars, and grades aren't a part of the process. It must sound weird to someone from the US, but it's a system that measures the sum of your learning, rather than all of your incremental progress. So, doing poorly during part of 10th grade won't affect your admissions chances if you study hard later on and learn the material. It's also a fair system: even Prince William had to get the requisite points to get into the course he did at St. Andrews.
Actually, I'd like to see a system like this in addition to a system that doesn't treat college as the only route to success. Skilled trades, for example, are very important too, and I think our society could do a better job of encouraging people to go into them.
This would leave a challenge for addressing other problems in the K-12 system, as it would mean abandoning admissions preferences based on gender or ethnicity or whatever. One approach that might help would be to let the money follow the child and to especially end inequalities in school funding. Ability grouping would probably help; kids presumably learn more when they go at a pace most appropriate for them. Career aptitude testing for 8th graders and 10th graders would also help (and is a lot of fun for the kids).
