I totally get the appeal of land taxes and restriction of land-use regulation at the local level, and by and large they seem like a reasonable approach to poor resource allocation and unequal ownership opportunities. One thing I've not seen addressed, though, is the apparent disincentive to improve communities in meaningful ways.
For instance, say I live in a very expensive city and I can no longer afford the land tax. I decide to move to a less expensive city and set up roots there. This new city is crummier: the city government is inefficient, there are fewer amenities available, and local institutions are poorly organized and executed.
I spend some time petitioning the local government to make reforms, I work with local groups to improve city amenities, and I vote for policies to revive local institutions. As I do this, the city becomes much nicer. However, it also becomes more attractive for other folks from the expensive city who can afford to buy up local property and drive up the value/taxes of my land. If this goes on, I'll once again be in a situation where I can't afford to live in my home because others want to live there too.
Say if, after moving to my cheaper city, I had instead decided to keep the city as crummy as possible while meeting my own needs. I drive a car, so I vote against bike lanes. I don't have young kids, so I lobby against school levies. I don't swim, so I vote against a public pool. This is objectively worse for the city as a whole, but if I want to be able to afford to live in a city that meets my needs these are the actions I should take.
There are always going to be tradeoffs between the opportunities of people who live in places and those who want to live in those places. Stringent local regulations weigh heavily in favor of those who currently live in places, and this is widely recognized (e.g. the term NIMBY is widely known). Land taxes and deregulated local zoning seem to weigh heavily in the opposite direction, but I rarely see this addressed or acknowledged. Moreover, land taxes in particular seem like they actively disincentivize pro-social or civically minded policies for existing residents (whereas local regulations allow communities to improve themselves without being priced out through other means).
If I'm missing some context here let me know, but it's one of my main critiques when these proposals pop up that I've never seen satisfactorily addressed.