Why? Because lower-price restaurants would have a choice: dramatically raise their food prices (which would almost certainly drive inflation across the board as everyone in all industries would hopefully see raises to deal with increased costs of living) or try to minimize the hit. If the latter, this would set off an immediate price war, even if unintentional, because McDonald's especially would strive to keep their prices from changing as little as possible.
Then, the smaller chains that couldn't afford to reduce their workforce and/or invest in efficiency or robotics wouldn't survive. You would see less competitive chains like Popeye's closing up on Interstate exits, and their marketshare would be handed over to the larger chains.
The unintended consequences of a massive shift like that would be enormous, and it would absolutely result in a stronger national chains and probably destroy or badly harm local eateries -- especially the ones that were trying to be price competitive. Get ready to see your local small businesses under severe pressure, while profitable operations like McDonald's and Chik-Fil-A will mop up the smaller places, and this is across the board at any low-skill, low-wage places, not just restaurants.