Well in most of US you can pay off the land but you still have property taxes which can go up. Also the tax basis can be adjusted based on the market value of similar properties in your area.
The vast majority of rent controlled cities have rent control boards where landlords can request and increase in rent in case of exceptional circumstances. In those cases, the landlord must show that the rent is not enough to cover maintenance, and the increase is granted.
In general though, maintenance on average only costs ~150-300$ a month, so it's not necessary.