Clearly, you do not understand how food stamps and Medicaid work. They go to the working poor who earn less than a floor amount. Working people still get food stamps, Medicaid and Sec. 8 housing. Those benefits are not reduced by earned income. They go away when the income surpasses a certain total level given the family size.
Again, clearly, the low wage job impacts the taxpayer because the wages are so low the employee qualifies for food stamps, Medicaid, etc. to supplement their low income.
You last two paragraphs are irrational. You talking about some supposed market mechanism that you think sets wages which is totally irrelevant to the discussion.
Food stamps subsidize low wages because every dollar the employer doesn’t pay we taxpayers do pay in the form of public benefits. If the employer was forced to pay a living minimum wage the employee’s total income would be increased to the level that he would no longer qualify for food stamps and our taxes would go down. We taxpayers are making up the difference. That what “subsidize” means.