I think technology is already on the way to solving this problem as more and more classes are taken online. Currently, those classes are probably still administered by mostly liberals, but I think the amount of political influence they can exert on line is significantly diminished, in part by the impersonal nature of the instruction but also because those professors know that EVERYTHING they say and do gets recorded and archived.
Eventually, there will be teacher-less online classrooms, and I think that will become common place long before driver-less cars. Of course some professions don’t lend themselves to this kind of instruction, but that tends to be in fields like medicine or engineering, which tend to be more politically balanced then all the humanities.
Unfortunately, going to a top-tier university is not just about the classes but about the contacts you make and the “club” that you join. Have you noticed how many high government officials are from a small number of universities. They hire and promote their own.
I wish that I could share your optimism about online education, but I don’t. I have seen liberal arts online courses where you HAVE TO give back the leftist answer that the professor is spouting or you will be given an “F.” When I checked the “ratemyprofessor.com” comments on these professors, other students said the same thing: give a leftist answer or get an “F”.