Another way to put it: the person who owns a vacant lot in Manhattan (worth many millions) pays the same tax as the person who owns an equivalent lot in Manhatt

Another way to put it: the person who owns a vacant lot in Manhattan (worth many millions) pays the same tax as the person who owns an equivalent lot in Manhattan with an apartment building built on it. They would also pay the same tax as the person who owns that same lot with a bungalow sitting on it. It's not regressive at all. You pay tax based on the value of the land. If you're not utilizing the full value of the land (by leaving it vacant or otherwise under built compared to the demand) then you're going to pay more in taxes than you get out of it. The whole purpose of LVT is to nudge you toward either improving the land so you can utilize its value or sell it to someone who will.