I hate that they use federal money to subsidize their workforce' paychecks (non-living wages, supplemented by food stamps), but...they're great for the consumer.
They are only great at the point of purchase. They make it harder to run a competing business, they create a tax burden by paying low wages, they distort local markets and cause local economies to suffer, they benefit foreign suppliers of products produced at wages and in conditions below American legal minimums (at the expense of American companies that compete with them, which affects American workers at those companies).
In order to avoid this you just don't let people pay less than a minimum survivable hourly wage so they can't force the government to subsidize them.
In the absence of a minimum wage constraint, and all other things being equal, a change in government assistance is going to result in an opposite change in the market wage rate. This is just a statement of market mechanisms. When the labor pool has access to higher benefits, it is easier for an employer to find someone willing to work for a little less than before (and vice versa).
The two situations are somewhat different though. In the first case you are talking about an individual moving themselves into a different market (unskilled/untrained labor to improved skills/experience, for example). Ensuring that this progression isn't penalized via overly aggressive reduction in benefits is a good thing irrespective of any minimum wage constraints. In the second case you are talking about a global change to the market constraints for all participants.
So I was just responding to the parent to say that when the government changes its "formula" for benefits, it is entirely reasonable and expected for the market to find a new equilibrium. This isn't an example of Walmart or any other employer "using federal money to subsidize their workforce". This is just the market doing what it does.
As for your minimum wage concerns, a minimum wage prices some people out of the labor market entirely. Someone with minimal skills or experience won't be able to bring enough value to an employer to cover the minimum wage. I think it would be much better to get rid of minimum wage rules and adjust benefits accordingly. It makes more sense for someone with minimal skills to have a job (and thus a path towards more skills) and some additional public assistance than to have no job at all and be 100% dependent on public assistance.
