This is a very sane point of course, and you are right that the consumer, and perhaps the low wage earner (in cases of the McDonald's type restaurants) now loses his extra wage to extra meal costs, so it is self defeating.

The problem though is that your costs are not driven up just by wage costs, but by many other things that are not helping the low wage earner. So the self defeating part of the "rising cost past to the consumer" is only a fraction of what makes life miserable for those who are at the bottom. Increasing there pay directly helps them 100%. And so it is still a net win.