The Georgist idea of unproduced means "unproduced by humans." But if we expand the idea a little to mean "unproduced by individual humans", then all social facilities are unproduced, and thus taxation based on their use is justified. Take for example the very large value of American residency: you get to live and work in America, with excellent defense, law enforcement and economy. People spend large amounts of money to immigrate legally or illegally. Residents make use of this value: why should they not be taxed for it as they might be taxed under a Georgist system of paying taxes on land they use?
Like most good ideas, this one has antecedents that go way back. Tom Paine had some similar ideas, that can be updated to be very much like mine.