This idea is pretty hard to square with economic incentives for infrastructure development. If the state builds a freeway or a fire station or other development, one major effect is that it enables a lot of valuable economic development. For public goods, it's hard to capture that value - even though it makes society better off, it's not worthwhile for any one economic actor to do it.
Property taxes (specifically on the unimproved value of the land) offers a way out of this dilemma. If you can do more valuable economic activity with a piece of land, you can and should pay more for it, so it'll be worth more. So if you spend $10MM/yr in financing for building a bridge, and it increases land value in the catchment area by $100MM, and you have a 12% land-value tax, the state responsible makes more money.
Property taxes (specifically on the unimproved value of the land) offers a way out of this dilemma. If you can do more valuable economic activity with a piece of land, you can and should pay more for it, so it'll be worth more. So if you spend $10MM/yr in financing for building a bridge, and it increases land value in the catchment area by $100MM, and you have a 12% land-value tax, the state responsible makes more money.