So what happens then? High enough property taxes could in theory result in a situation like Detroit where the land value drops so low that properties are abandoned, with no buyers. But that seems unlikely in California?

At less of an extreme, there are still buyers, but they offer less money so they can still make a profit. So, the property tax basically comes out of land values. The current owners lose money on the property. It's the opposite of the windfall profits that California property owners have gotten from rising land values, taken out of whoever owns the land now.

For the next owner, their mortgage expense is lower, their property tax is higher, and maybe rents and profit margins stay about the same.

Notice that if the demand is there, falling land values doesn't result in lower rents. If your complaint is that the rent is too damn high, higher property taxes won't fix it. Only more housing does that.

I'm a bit skeptical that it would really work out that way. In California, we can have the odd situation where the current owner pays low property taxes, the new owner will pay higher property taxes, and yet property prices get bid up, and whoever buys it has to pay both more property tax and a higher mortgage. But they can still afford it, because there are a lot of rich people out there.

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.