Fine, you want a policy that's better than the one described in OP but feasible on a small scale? Have the city buy up land and rent it out at market price. All

Fine, you want a policy that's better than the one described in OP but feasible on a small scale? Have the city buy up land and rent it out at market price. Allow any kind of housing to be built on top of it, have no requirements for income etc. Then use the profit this produces over the current system to directly subsidise low income households. This is more efficient and has the same subsidy effect.