The cost of police, fire fighters, schools, roads, etc. don’t go up with the value of the home. There is no reason that you couldn’t charge a flat rate to every property owner - including businesses.
The cost of all of these things do increase with the value of the home, because the labor required to do it gets more expensive. The individual house price doesn't contribute to this but overall housing costs do.
SF has had an explosion in property values and thus struggles to find teachers, firefighters and police officers at the salaries it's willing to pay.
How so, taxes are meant to fund the government and services they provide. Everyone who lives in a jurisdiction either consumes those government resources or we as a society have decided that it was in the common good to provide those services (ie education).