Nah, nonprofit state-run landlords
We have those. They run "Section 8" housing, which, in my area at least, is substandard housing in high crime areas, because those areas have the cheapest housing, and that's what the state buys. They also currently have a 6-year wait-list in my area. You only have a fixed time you can live there. There is means testing, and strict rules on who can come and go.
The problem isn't actually the "state run" part, though. The problem is the market in which the state is operating. Whatever approach we take, we need to fix that market first, and that's what I'm talking about.
I don't want to buy a house, I move around a lot...
I don't think you understand what a "land contract" is. It gives you the flexibility you need from a rental agreement, without imposing rent on long-term residents of a property.
If you are only going to be living in the property for less than 3 years, it is a rental agreement. It is an agreement that happens to be recorded with the county, like a deed, which allows them to consider you an "owner occupant".
The real differences are if you decide to stay there longer than 3 years. Your monthly payment was calculated by assuming principal, interest, taxes, and insurance on a 30-year mortgage, which is usually what you're going to be paying in rent anyway.
If you stay at least three years, the agreement becomes a sale contract; you become the deeded owner; your equity becomes the down payment, and your former landlord becomes a private lender with those pre-existing terms.
If you leave before 3 years, you forfeit your equity, and the agreement functioned identically to a rental agreement.
You still get to live like a tenant, and move around as you like. You can unilaterally abandon the contract for any reason during that 3-year period. For you, nothing changes other than the words at the top of the agreement. Words that are important to your "landlord" as it saves him a lot on taxes, but that are completely irrelevant to you as a "tenant".
But, if you do change your mind during that three year period, and decide you do want to become a homeowner, you're already well on your way.
Alternatively, Duplexes, triplexes, and quadplexes are all single properties, where the owner of that property can live on site, making the property eligible for the owner occupant credit. The other 1-3 units on the property are available to rent out. If you really want an actual rental agreement instead of a land contract, that is one option.