I guess the problem with that scheme, or any subsidized scheme, is that it relies on the tenants getting into higher-paying jobs eventually.
At the rents that most public-housing residents pay, it would take them forever to pay off a construction loan/mortgage on their unit. And when their food, housing, and everything else is subsidized, where's the incentive to work harder, go back to school, or otherwise improve their income? Obviously, their standard of living is fairly low, but with no danger of homelessness or starvation, the impetus to improve their economic standing is much lower.
I realize I sounded pretty conservative there, but there is in fact a noticeable drop in real income that's created as people start to earn more money, but get stuck with higher taxes and qualify for fewer government benefits. That drop (the
"poverty trap") acts as a big disincentive to aim higher.
Even if they could eliminate the drop, there's still a range of incomes at which an increase in income yields no net benefits.