The government already takes a certain percentage of our income; and the more you make, the more they take. It follows logically that they should pay for our education.
Of course, as with healthcare, the rest of the world figured this out a long time ago.
The problem is that an individual school does not get rewarded based on how well it educates the students (except perhaps for private colleges who make money from alumnae donations). Ideally, you're education tax dollars would forever go back to the school that educated you. That way the school would have an incentive to train you well.
This incentive does not exist today, either. To even hope to stay financially solvent enough to remain in existence, universities have to direct their resources towards research, not teaching. Having researchers teaching classes annoys the researchers and the students. But since it's the only way the system can work, it is tolerated.
Maybe that would be an improvement, but it sounds far from ideal. In today's world, the school would then have an incentive to send its students to Wall Street and fuel even more financialization.
Of course, as with healthcare, the rest of the world figured this out a long time ago.