Yes, technically this is all correct (as articulated by Modern Monetary Theory). The obscured point is over whether humans need some form of disciplinary constraint in order not to self-destruct. History suggests they do. Our democratic governments and citizenry are so constrained financially by the cost of credit and that is what we have removed from the public sector.
So the problem is always if money is free, what is to prevent it from being wasted on unproductive activities? Merely providing resources for education without cost is no guarantee we will actually get productive education. In fact, the costs of a good education would likely continue to balloon beyond all rational reason, eliminating it as an option for a majority of our children. When I was an undergraduate the most expensive private school tuition was $5K/year and that included room and board. The CA 529 program for my daughter projects that cost to be over $800K for 4 years of private and $600K for 4 years of public university education. And that’s after spending almost as much on private elementary and high school! This is a joke that only becomes credible if we destroy the true value of the currency.
There is no free lunch and public finance can’t provide it. MMT fails to consider the human behavior factor.