It won't grind to a halt. The owner will sell, because they can't make the business work.

At what price will they sell? At whatever price a buyer who thinks will make it work. And by "work" there are many definitions, from continuing operation at current rents, to building more units on the land so that it generates enough income to pay the tax.

Land value taxes shift tax burden away from productive use of land and on to unproductive uses of land. The people who pay more are land speculators and those with empty lots, and the people who pay less are those productively using the land, which is 99% of homeowners and businesses.