I don't think it's workable - while there are some wards that have both FC housing and private, there are also private only. What this would do is actually worsen the situation for private housing, as private houses in private only wards would be scooped with the intention making them into FC's houses.

As it stands currently *small* houses are less desirable, and attainable for a private residence - they would also become a high demand property with such a change imo.