Hmm, that's a good point.
Though, wouldn't an LVT that encourage companies to push all their employees to work from home, where possible? There are certainly benefits to that, but it might mean that certain industries get taxed much more heavily than others. Is it ok if distributed work-from-home software companies pay no tax at all, because they have no offices? The workers would pay tax on their own houses and apartments, but the company wouldn't.
I guess it depends on whether you want to consider taxes to be a tool for limiting rent on scarce resources, or for balancing out wealth disparities. (aside from the main goal of raising revenue, of course) The two things are related, but not identical. The first seems like more of a proxy for what we actually want to do, which is to prevent concentration of wealth. Or is it more about the fact that collecting rent isn't an economically productive activity, so if we incentivize everyone to gain wealth by producing value, it'll make us all wealthier?
To be fair, the hurdle that LVT has to pass is not to be perfect, but just to be better than what we have, which isn't a high bar. But it is worth thinking about the possible loopholes and edge cases.
Should we also assume that switching to a single tax wouldn't exclude things like cigarette taxes and carbon taxes? These taxes are designed intentionally with particular incentives, just like the LVT, and unlike property taxes and income taxes.
It would be a shame to take away the single best tool we have for fighting climate change, for example.
Anyway, no obligation to reply, a lot of these questions are just me thinking out loud.