I am extremely wary of n=1 reasoning. It ends us being confirmation bias. We look at Sears, note that they pay more than Walmart, and say that paying employees more either has no effect, or is harmful.
But are we also looking at the thousands of businesses that pay their employees terrible wages, but go out of business?
Businesses are complex systems that defy the search for simple explanations. That won't stop humans from trying, though. We all love the idea that there is some simple Eureka! idea that explains everything.
In this specific case you're talking about wages as if all other things are equal. All other things being equal, if we pay employees more, we lose business to lower-cost competitors that pay employees less.
This is like saying that if all other things are equal, a restaurant that pays more for its ingredients will lose business to competitors that pay less.
Of course, as managers, our entire reason for existence is to make sure that all other things are not equal. If we pay more for ingredients, we have to build our business around turning those more expensive ingredients into a better customer experience and perception of value.
And the same goes for paying more in wages. It's our business as managers to turn that into value. If we can't, are the wages the problem? Or is our mismanagement the problem?
Looking at the comments about shopping at Sears, I am not seeing a lot of "Everything about Sears was great except things cost a few cents more." I'm seeing anecdote after anecdote about how poorly it was managed.
Under the circumstances, if I wanted to cut wages at Sears, I would have started with their managers. If they're going to manage the thing into the ground, why pay them more than you'd pay an intern in an MBA program?