Not just neighboring parcels. Any improvements on one's own property (separate from the land itself) would be factored into LVT through an indirect tax on improvements via a higher assessment value. While certains areas can be "nice", not all homes in a given area are equally "nice". Some parcels of land will have their values "propped up" by the home that is sitting on it as well as proximate homes while others are "weighed down" in the same manner. This would result in unequal LVT assessments even for parcels of the same acreage and quality within a given area. As a result, It's difficult to assess the "actual" land value seperatley. From this, one can conclude that an LVT on a parcel with less valuable property or (a property proximate to less desirable property) plus an improvement tax can be lower in cost than an LVT in on a parcel with property that is more in demand.
> In reality, the niceness of surrounding homes is hardly a factor; proximity to economic centers (be it directly or by proximity to rapid transit) ...
Homes can be valuable precisely because they're located away from economic centers. That too is geography in action. And if COVID telecommuting is an indication of market preferences, home-owning adults prefer small, out-of-the-way towns with plenty of space, low property taxes, and good internet connections. So I'd hardly think that proximity to economic centers (usually cities) is as relevant it used to be.