Part of Sanders' argument relies on the belief that there is a possible free lunch, here : they believe WalMart could raise wages significantly without causing the company to explode, either not harming people in ways that count to the progressive movement (decreased profit to corporations) or by arguments of comparison to CostCo, Trader Joe's, or other stores that have different structures. I'm pretty sure the math doesn't work out that way, and the realistic event chain is likely to be drastically different, but it's a very common belief. From that perspective, it's more the concept that WalMart's low wages are a bad equilibrium point established by existing laws, and because it is less costly to the state for WalMart to directly pay more at a different equilibrium, the state should force them to change their actions.

If it helps, almost all of the people opposing WalMart on this tactic have called for increase welfare states of the type compatible with what you've suggested. It's likely to complicate getting interest from the right-wing in the United States, but since the right consider work requirements one of its biggest successes there are some much more pressing issues with trying to get them to accept a basic income guarantee.

((On the flip side, I think there are some issues with BIG or BIG-like systems that make them poor solutions to gwern's concerns, but these probably exist outside the scope of this thread.))