That's an interesting way of putting it -- "the house itself pays the taxes". I guess you mean the solution I favor, which is to allow the property owner to defer some of the tax until the property is sold. I suggest that Prop. 13 in California, for example, should have limited not the growth rate of the tax, but the growth rate of the amount that actually had to be paid in a given year. The balance would be covered by a lien due at sale.
This is already effectively how it works -- it's almost unheard of for a local government in California to kick someone out of their primary residence they own because of back taxes.