Why not just tax the land value and disregard the things in top of it entirely?

One reason would be that it is the things on top of the land that determine how much of various government built and maintained infrastructure is needed.

Income tax is inherently progressive and doesn't hit Grandma who lives on modest retirement and social security.

Having one reducing reliance on property taxes

"We've got a bunch of people with massive wealth, so tax only the people earning new money" doesn't sound like it is going to equalise the state of the world.

I will also accept inheritance tax at 90%, if you really want to skip property taxes :)

I'm perfectly open to a wealth not just inheritance tax too

Do want California's housing situation? Because that's how you get California's housing situation.

California's housing situation is because they are a highly desirable location and didn't build enough housing to meet demand not because they have an income tax.

Selling your house and losing your lower assessment is a huge reason not to sell your house. This make California’s real estate market less liquid then other real estate markets, since selling can have a huge extra cost vs not selling.