But at the same time you don't want to squeeze people who have lived in a particular location for a long time simply because the neighborhood is gentrifying. One proposal that I liked more than the LA proposal is to simply tax additionally properties that are not someone's primary residences (checked against address on the California tax, for example).

If only the land were taxed then people can simply move from overpriced single family homes into denser construction to amortize the land tax over multiple units.

If only land were taxed, single family homes would probably not even exist. They'd all eventually be torn down and replaced with apartment buildings as dense as the law allowed. Not a great consequence either.

The need for city services (which property taxes fund) tends to scale more with population size, than with land area.