What that allows you to do is more aggressively tax the land--faster readjustments, and with a much higher tax rate. To the extent you do this, you incentive more efficient land use. But in practice jurisdictions don't do this. If you read the literature on Pennsylvania and Mexicali it becomes clear that this isn't politically viable, and so LVTs there are watered down w/ tons of exemptions and a very skittish assessor's office, and don't actually behave much different than regular property taxes.
Lo and behold, when I dig up the details on Estonia I find the same thing. AFAICT, 1) principles residential homes are exempt (specifically, the land the principal residence sits on). 2) The tax rate is capped at 2.5%, but can be as low as 0.1%. I'll bet that property reassessments in Estonia aren't particularly aggressive; but even if they were, 2.5% isn't very much for just the land value. The median rate in the U.S. is 1%, but that includes land value and improvements; and is as high as 2% in some places.
LVTs just aren't politically viable. When a property assessor's office is faced with reassessing the value of land in a way that forces existing homeowners to sell, they're just not going to do it. And even if they tried, a pro-Georgist LVT assessment tends to be much more speculative because they need to guess what could be built on that land, not what is actually being built nearby. Where they've tried to do that, you either see corruption, a "reluctance" to reassess (see Mexicali and elsewhere), or voter revolts. This is very much how California got Prop 13--the fear of reassessments forcing people out of their homes.
Don't forget, a regular property tax can also be used to promote densification. In theory it's not as efficient, but in most cities vast swaths of land have uniform density, so this efficiency concern isn't implicated nearly as much. And yet, predictably, attempting to use property taxes for social engineering always falls flat. Threaten the [perceived] security of family and retiree homeowners and see how well you do in the next election. All the promises of a better, more equitable future won't save you.
I bet if you look at how LVTs are implemented in all those other countries given by Wikipedia, you'd see the same thing: an LVT in name only, a pliable assessor's office, giant loopholes, etc.