Worker productivity increases cannot be legislated. Such productivity increases can only come from workers improving their skills or technology that increases their productive output (as simple as an electric drill to as advanced as an exoskelleton with a HUD). Minimum wage laws are effectively bans on low-productivity workers. By making labor artificially expensive through legislation, demand for it drops, total economic output decreases, production costs increase. There's no reason to believe that the home-production industry would be able to reduce costs / increase output with minimum wage increases; in fact that opposite is the case.
Legislation can only reduce the permitting costs of housing production IFF it becomes more permissive. In the regions of the US that I'm familiar with, all the areas that have high housing costs pass legislation that increases permitting costs or transactional costs to bring housing to market. This can only result in a price increase globally with some politically-connected group receiving a benefit.
Legislation and corporate-bank policies artificially increase the money supply to the greatest degree with housing loans. Typically these workers are not minimum wage and in addition to the above effects, the Cantillon effect gives an undue subsidy to these higher wage workers https://www.aier.org/article/sound-money-project/cantillon-e...