No what happens is people living in more progressive areas get more progressive education, people living in more conservative areas get more conservative education.
Far from true.
Almost every university is populated by the same sort.
Every poll of professors shows the same bias.
The result is a body of graduates with knowledge, but without wisdom.
You don't want people to have an education, because educated people are, by and large, liberal, and not just in the US. It's not because education has a liberal bias, it's because the history of the world is one of overcoming conservatives of the era, and pushing forward new ideas.
History is always the victory of the new over the old. Whether that's a good thing, depends on the circumstances.
The Founding Fathers were liberals because they refused to accept the status quo, and wanted freedom. Freedom is a liberal concept.