"the value the owner derives from the house is not dependent on the resale value of the house"

An owner can derive value from the house in one of three ways:

A) Occupy the whole place.

B) Receive rent from a tenant.

C) Something in between (e.g. airbnb one room).

When property prices double, it's likely that rents roughly double. This may not increase the value the owner can derive from (A) but it will sure change the value they can derive from (B).

So they might decide to switch from living in the place to renting it out. If they don't decide to switch, then it indicates the value they derive from living in the property has either gone up, or it was always way higher than the market rent.

It seems like market rent is a reasonable benchmark to use to calculate property taxes, and property value is a reasonable proxy for market rent.