These are fair questions and I don't have real answers, just opinion based on having a good deal of exposure to other cultures and systems.
I believe one of the misconceptions in the US is that free university in other countries means anyone gets in. That is simply not the case. A very simple example I have of this is the daughter of one of our close friends who wants to study medicine in Spain. She has been preparing for a full year to take entrance exams in order to be accepted into the university. Her parents are paying for her preparation to pass these exams. Even if preparation was free, the acceptance rate will be based on how many seats are available and some weighing of results.
This means that only a certain type of student (notice I did not say class) will have access to university education, even if it is free. I get the sense some Americans think that making university free means everyone has an equal probability of obtaining a PhD. This is a fantasy. Universities can only accept a certain number of students per year and they have to filter from the total candidate population in order to reduce it down to what they are able to handle.
It is hard to argue against the potential value of free education except to point out that, at a first level, if unworthy students are accepted at the exclusion of good students we would be wasting money and valuable resources. If we are going to give someone the gift of a valuable education they have to demonstrate they are ready for it and that the probability of success is reasonable.
This, in the US, would setup yet another inequality problem. It is easy to see that kids from more challenging environments are not going to do well if they have to pass tests in order to enter Harvard or MIT when it is free. Do you exclude really good students to accept those who are almost guaranteed to fail? Why is it OK to discriminate against kids who are excellent students? Why is it not OK to tell less capable students to spend a year or two at an (also free) preparatory college and then take the entrance exam again. In other words, don't degrade standards for some misplaced social ideology. If we want to graduate excellent doctors, let's do exactly that through a process that ensures it.
And then there's the problem of how to pay for all of that. Universities and colleges in the US currently exist under a system where students are paying anywhere from, say, $20K to $60K per year --if not more-- for their education. That means that, as a business, as an organization, their financial model is entirely based on the various revenue generators available to them, one of which is tuition. This financial model cannot be supported if tuition disappears. There is no way we can pay for that structure through taxation, even if we take all the money from all the billionaires in the nations (which is another massive lie these politicians are telling).
To this point, one of the other things Amercian voters without exposure to other parts of the worlds don't understand is that universities in other nations are not as rich as those in the US. Professors don't get paid nearly as much in free-education nations as they do in the US. I mean, in the US salaries in the hundreds of thousands of dollars per year --even millions-- are a very real occurrence.
https://thebestschools.org/magazine/highest-paid-college-pro...
Outliers? Sure, but the reality of the matter is that free-university professors, in the US or elsewhere, simply can't make as much. The equation very quickly becomes mathematically unsustainable. However, it does not end there, there's staff and an organization behind each professor and class and those have budgets too. Simple put, if less money comes in you have to either close down or spend less.
As you noted, things are far more complex than they always seem on the surface. We can't have free education for all without addressing costs. There is no way we are going to pay a professor hundreds of thousands of dollars or even millions if taxpayers are paying the bill and everything is free. At some point things have to be fair and reasonable.
Simple example, my son is at a university studying robotics. They have a two million dollar humanoid robot in one of the labs. They also have equipment and other robots costing many, many millions of dollars. These costs have to be paid somehow and by someone. My guess is that, today, that's a combination of tuition and donations. If we make tuition free, the need for cash can only be reduced by lowering professor salaries, reducing the size and breath of the organization and controlling the other costs (no million dollar humanoid). This is a reality at universities all over the world, they can't afford to be government-funded and have the same kinds of extravagant things we often see at universities in the US.
Can it be done? Sure, of course. Be we should not lie about how we would do it, and this should include a conversation about how our universities would change, how salaries would change and how access to technology and resources would change.
Yet another level of detail: What does "free" mean. In Europe and Latin America you might have free university but the cost of books and the cost of living somewhere and all of your personal costs are still yours. In the US, unlike in other parts of the world, kids leave their parents home and go to university all over the nation. In other countries is is very common for kids to go to local universities and stay home. Well, if our universities are free, who is going to pay for a kid from Las Vegas to travel to Boston and live there while attending free Harvard? That is still a significant amount of money. And that should not be a part of "free".
All of this means that, even if we make university tuition free you are going to have to filter kids based on academic performance --creating a social inequality battle-- and you are not going to pay for them living at some far away city at all. Again, things are always far more complex than they might seem on first inspection.
I don't know what the solutions might be. My gut feeling is that, in the US, the first step is to get government out of the business of financing university education. That will force universities to compete, control costs and become more efficient (financially speaking). If we do that, tuition will come down and might become very affordable. This could resolve the problem to a satisfactory level as a first experiment. Allow a natural reduction of cost through competition. Ten years later, come back and consider the idea of funding the more efficient versions of our universities to cover, say, half of the tuition. Another ten years and we cover it all and university is free. I would much prefer to see a gradual, logical and careful process towards better and cheaper education than some mathematically impossible attempt that is far more likely to cause a disaster than to fix anything.