Ryan, I think you’ve just made an excellent argument for increasing the minimum wage to a living wage, which, by the way, should include a requirement for employer-supplied health insurance coverage.
I made a parallel (sort of) point in my article Hypocritical Conservatives Want Taxpayers To Subsidize Their Business Costs that by paying less than a living wage businesses are shifting their obligation to pay the real costs of producing their products to taxpayers by forcing the government to subsidize the housing, food and medical care costs for employed workers.
This below-living-wage tactic allows them to sell their products below their “real” cost of production, i.e. the price they would have to charge if their employees were paid enough to live on without government subsidies.