The part that's missing is that much of the market value of property in the city comes from having these public buildings in place. Libraries, hospitals, transit stations and so on could be funded entirely out of the value they add to nearby homes and business land - it's just that value can't be captured so easily, because ownership is diversified. A land/property value tax that was applied equally to public and pri…
A land value tax would also put the onerous cost on citizens nearby and make rents and property cost even more. Then you would probably see a stream of subsides come in to support low income renters.
It seems like it is a much more intrusive government solution with a lot of downside.