I'm fairly sure the point of air gaps on drainage is to prevent sewerage water from backing up in to appliances if the sewerage line is blocked. It will instead spill on the floor where it will be more easily noticed and cleaned.

That is exactly why they are required in restaurants. You wouldn’t want the sewage to back up into a sink where food or dishes might be.

That’s exactly what it’s for. If you block the sink drain and fill it with water, you can have water flow down the dishwasher drain hose and into the sump in the dishwasher. If that happens during the rinse cycle you’re rinsing with grey water.