In any case, the real reason for the article and its complaints about a "tight" labor market is to lobby for low wage immigration:
"Our industry is very much in need of a temporary visa program for the low-skilled, essential workers,” said Shannon Meade, the National Restaurant Association’s director of labor and work force policy. "
Translation : pretty please send cheap labor our way; our profit margins aren't high enough.
Switzerland seems to have achieved some balance in this regard. Japan too, although their wages are artificially depressed via other means.
I actually really loved working in a kitchen but it's absurd how bad the labor conditions are.
Demand functions aren't generally straight like the illustrative graphs used in intro classes. What you end up with is easy replacement with similar goods. Being able to differentiate goods in food-service seems like a very difficult proposition without some sort of brand recognition. Because of that, if someone can purchase some food that is equal or close enough to equal at a significant (significance as defined by the consumer utility) then they will go with the cheaper option.
While raising prices seems like the simple solution to this issue, the reality is likely that they would quickly - if not immediately - price themselves out of the market.
I think the restaurant industry should look more holistically at options for dynamic pricing ala Uber. These could increase their margins enough to actually address the labor costs more effectively.
(Not an economist, for the benefit of anybody who doesn't find that patently obvious ;-)
ETA: I don't see the reason for the downvotes on the parent. It seems like a pretty reasonable explanation as to why there would be a brutal race to the bottom in restaurant industry. But again, my economics background is limited. Maybe somebody could explain the flaw in the argument?