The way I understand it... If Alice owns land and sells to Bob with some restrictions, that means Alice is still maintaining some ownership of the land. And the price that Bob pays is discounted from the otherwise fair market value, because it has those restrictions on it.
Then, if Bob sells it to Charlie, Alice still has an ownership stake (logically speaking) from the restrictions (whether it is land use, or mineral rights, or whatever). That is what keeps Charlie bound by those same restrictions. And again, the land isn't worth as much to Charlie as unrestricted land would be.
Now since Alice still has what could be considered ownership in the land (via the restrictions), then Alice should be paying some property tax based on that value she is retaining. And since taxes can be assessed based on the nature of how the property is used (such as granting a homestead exemption/discount for example), then if the current situation isn't benefiting the county or city, they can redefine their tax code to raise the portion that Alice would have to pay based on the ownership type.
I understand that the above is an ideal situation, and if Alice isn't getting a tax bill then that should probably be addressed by the local government.