1) You're assuming the educational institutions themselves are engines of anti-fascism. But plenty of very fascist ideas have come out of universities.

2) You're ignoring communism and the far-left. Plenty of disastrous ideas are produced in a vacuum by intellectuals at universities. To give just one example: Khieu Samphan, was educated at the Sorbonne. His ideas lead to the deaths of a quarter of Cambodia's population.

3) Even if we give you 1 and 2, where do you stop? How much money should be poured into education (esp if it's the taxpayer)? Resisting fascism seems like one of those infinite 'our work is never done' things that have unbounded demands.