There are a variety of systems that 'work' around the world. The United States' model clearly works to some extent as its universities are still able to attract talented professors from around the world and produce a lot of great research.
There are a few reasons why people would resist the idea of making all universities publicly funded. One of them is that Academic pursuit is now beholden to the state and its interests. In the current system, you can find funding for research in universities from both private and public investment. Also, when all funding is from the government, its bureaucratic nature tends to increase costs. Anyone that has worked with a government contract in the US probably understands how lucrative it can be because the government is not incentivized to reduce costs in a way a private entity would. Anyone that has worked in a department of the government when they have to spend the rest of their budget so it doesn't get reduced also understands this. Interaction with private entities that are incentivized to increase profits with what is basically an infinite money pit is dangerous (who then use said money to push for regulatory capture in congress), and you can see the effects of this in almost every aspect of the U.S. government.
It also further cements the idea that you must go to University in order to be eligible for any sort of job in the U.S. Jobs that traditionally only required a high school education or less now require a 4 year degree. This already is happening to an extent because it's an easy way to eliminate candidates, despite the fact that their profession may or may not require any sort of post-secondary education.
It also is a program that benefits and subsidizes people that either don't need it (wealthy upper class) or are already relatively advantaged in life (middle class). It would unlikely benefit the poor as much as you'd think, as there are still a lot of barriers to getting into higher education that the poor face that the middle and upper class simply don't. From the bottom up they have worse schooling and less opportunities. They may be under pressure to find a job immediately out of school (or drop out of high school) to support their family. The exceptions that can benefit from some program like this likely already can benefit from the current system of scholarships and grants to underprivileged students.
I would like to see a shift to something more similar to Canada where the distinction between college and university is clear. Academic and Vocational (but still professional) schooling being separate can be valuable and serve students with different learning styles better than the largely liberal arts education that universities in the U.S. provide. I'd also like to see some of this theoretical money that is funding tuition-free university towards improving educational opportunities from the bottom up in places that desperately need it. It doesn't matter if your postsecondary education is tuition-free if you can't make it to college.