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Individuals and corporations both rent out houses/apartments to get more money out of it than by selling it again. Your model would absolutely lower the return on renting property out. So increasing the rent would be a logical decision for them. Or if your rules make renting unprofitable, noone will build more houses/apartments than their own. Sure, the house market might see low prices, but at some point it might be more logical to hold the property than to sell for a very big loss, hoping for better times. So a lower limit would be there. Then you have many non-sellable homes sitting around and still many people, who cannot afford to buy but also cannot rent (since nobody rents out anymore).
One interesting thing in your scenario would also be, how to handle the part ownerships. Lets take a student at the university renting a small room/apartment for the time of their studies. They might make payments towards ownership for a few years, accumulating something like a few percent of ownership. Then their studies are finished, they move and another student comes in. Rinse and repeat. You will get property owned by tens of persons this way, even when not every tenant wants to do the payments. Would be a hell to administer. Nothing would work anymore regarding decisions and work relating the property.
I think nothing can work around the fact, that we need many and good publicly owned properties for renters, where the rent is no driven by the profit motive and in effect is decided in democratic structures (like city government). Maybe in your scenario you would also want public entities buying homes to then rent without profit.
Eh, Wonderwall sounding right is really not a kid level song. I struggled for some time with it. Lady in Black is the absolute beginner song. Good for practicing a 4/4 strumming pattern and 2 of the easiest chords (Em and D).