How would your friend feel about property taxes that scale with market value, but can be deferred until the moment the home is sold, at which point the deferred taxes are paid from the home's appreciation? We could even add a provision capping the maximum tax bill to the actual amount of appreciation since the home was bought. That way nobody is priced out of their home, but the taxes to pay for services that everybody uses are still distributed equitably among all residents.
Housing changes hands much less because the tax gap means all other factors things being equal the house is worth more to the seller than the buyer - they can't live in a similar place for the same money. Deferring taxes just makes that gap in value bigger. And there's not necessarily a point where the city gets money for services, tax rates are passed down with inherited housing.