I can't comment on the narrative, because I have no involvement in Georgist discussions and communities, but I have a few observations on why the deeper appeal exists in the first place.

1. The general appeal, to me, of any tax proposal is the degree to which it generates needed revenue for governments while supporting the likelihood that private sector decisions promote overall prosperity. Taxing a thing (or service) makes it costly, which promotes efficiency or avoidance of its use. This is reflected in direct consumption habits, but also in higher order effects like how much we invest in scaling up production, training skilled providers, inventing better solutions.
2. Land is one of the few things in this world that is truly finite. Accurately valuing it is tricky and a moving target, but to the extent you can do so, it is close to minimally distortionary and maximally supportive of overall economic growth.
3. Pigouvian taxes and subsidies are either intentionally distortionary (we don't like X and want less of it even if this is economically inefficient) or a way of reducing distortions (forcing actors to internalize externalities).
4. Any significant change to how taxes work is going to generate significant changes in the market prices of many, many things, depending on all the things like elasticity of demand, ability to find substitutes, a bunch of other laws that were already on the books, etc.
5. LVT without corresponding changes that loosen rules restricting what people can build where, and how, is not going to have the optimal impact, to say the least. Doesn't matter if you have high LVT if the local planning and zoning agencies flat out refuse to let you build. Of course I could frame this as "Land value is extremely distorted by other regulations that close off higher value ways of using land."
6. It's not just about "increasing density." It's about promoting the right density and zoning and etc. for a given place. A piece of land in the middle of nowhere is easy to value. A piece of land in a dense city has its value determined by everything around it.