Most people are paying rent to a bank, not the government.
There is nothing special about government collecting coin vs a private entity. Rent as commonly definied has component of:
1. making payment to a "master"
2. obtain use of something in exchange for that payment. Property taxes vary, but $3,600 a year, or $300 for a "lower middle-class" place is not uncommon.
3. Defaulting on payment can trigger the "master" to boot the possessor of the property to leave in a very formal process that is slow.
If one pays off the entire amount due and clears themselves of a mortgage, the internal compulsion to pay the taxes to avoid tax liens is greater than someone with a mortgage partly paid. The property would get auctioned off for much less than the what the owner sunk into it, thus the surplus the owner gets if he doesn't redeem the property would result in a big loss, if anyone is alive or aware to claim that surplus.
My mom owns her property with no mortgage. The property taxes are still an obligation in perpetuity, and so are the HOA dues. Thus, even with hundreds of thousands actually sunk into the "purchase", loss of title can be forced if for whatever reason, the payment doesn't get made.
Whereas with other things that are "owned", paying off in full usually entails full control, no further payments, and no intermediary forcing transfer of the goods to another due to the "periodic usage fee".
The bureaucratic arm of the government is the most predatory fund-seeking, because unlike the votable arm, the hired hands like attorneys, social workers, police etc do not have effective mechanisms for removal in case of small abuses. City attorney violates a law? Violated has to pay the appeal fee first, pay a lawyer for legal advice, then get the hearing done, and if the violated wins, the city just has to pay costs to the other court, etc.
Bureaucratic misconduct is desirable to government because it increases revenues with no penalty, and if a penalty does come around, the crony industry of lawyers benefit from economic stimuli out of the need to try to battle against the government.
As a tidbit, some places in the states allow for a "ground rent" arrangement, like around the Baltimore area.