Rent-to-own in general exists as a concept in many places, but it has a sour reputation due to the predatory practice of vanishing equity. Essentially, a renter is sold on a higher rent price on the premise that it will result in their eventual ownership. However, if they fail to make rent or must leave early for various circumstances, they have no equity to recoup. In some cases, this serves as an incentive to force out a tenant, and in worse cases, that's the design of the scheme from the beginning. Government housing programs tend not to fall under this category, but I have heard of some governments (e.g. Singapore) revoking housing rights without return of any capital as a penalty for certain violations.

Yes, under capitalism, everything that can be corrupted will be corrupted. This generally seem to be less of a problem for the nordic countries somehow, probably a combination of strong regulation and a culture a bit more geared towards fairness.

BTW, Singapore has an home ownership rate of 90%, so it seems like a big success.