The only alternative to partial subsidies for poor workers, is total subsidy (which is what happens if you try to make Walmart pay workers $20 / hour, tax payers end up paying for a total subsidy as those workers lose their jobs). That is your only choice. Highly developed nations in eg Europe also follow that exact model, despite their very advanced welfare state systems. Do you think the bottom 1/3 of workers in Britain - given how much lower Britain's median income is versus the US - are paying their full way in terms of costs via their very low incomes? No, they're being subsidized. Their healthcare and numerous other government benefits are being subsidized by richer people via taxation. The same is true in France and Germany as well, and essentially all developed nations.
The Medicaid and food stamp programs you reference (the part that are partial subsidies to Walmart), are overwhelmingly paid for by the top 1/3 in the US via taxation, just as in most developed nations. What exactly is your argument against that? You'd rather force Walmart to fire a million people courtesy of aggressive automation, by raising wages on them, just so the very well off top 1/3 aren't put in the position of having to subsidize that labor (to the benefit of Walmart shareholders, which are overwhelmingly made up of the tax payers footing that subsidy bill to begin with)?