A well run government subsidized system still has choice and competition. In belgium I can choose what school my kids go to, even though all of them are subsidized to the point of costing very little. I can also choose what hospital to go to, or what doctor to see, and that visit will always be subsidized by the public healthcare system, while doctors still are self-employed and can set their own rates (higher rates means I pay more myself). In both systems there is little administration, because the system works the same way for everyone and is straightforward.
Sadly in the USA, any hint of allowing “choice” with public schooling has you labeled a heretic by one side of our two-party system. While leftists despise monopolies in all business, they worship monopolies when it comes to schooling, no matter how expensive and how terrible the outcomes.
