This is an area where I veer hard right (or off on to some weird Z access). The morality that says the government has no business telling consenting adults what they can and can't do in the bedroom or whether anyone has the right to take their own life is the same that say employment is a private agreement between two parties.
When you say companies should not have employee's on food stamps, I understand your take from an ethical perspective: I don't want anyone on food stamps, either. But the company doesn't care about that and honestly they shouldn't care about that. Companies will always pay you less, they are incentivized to pay you less. Individuals are incentivized to want to make more. If able bodied people don't want to be on food stamps then I suggest they not work at a place that puts them below the poverty level. This is also why I support unions - just large groups of people trying to leverage themselves to better salary. Don't want to work for a place that has a union? Good news! You don't have to.
I think the thing a lot of people miss when it comes to setting wages is that anything you do to try to intervene on behalf of the worker will ultimately stratify that job. The free flow of wages and people shifting jobs is the best way to get people off food stamps.
Taxes and wealth are other subjects entirely, but I always feel compelled to speak out on the negative unintended of minimum wage hikes/'livable' wages. You will ultimately hurt the ones you are trying to protect.