The reason for an air gap is overall safety...it is safer than just a high loop. Water and waste will take the path of least resistance, but throw in a disposer which can act like a pump, and stuff could go places it wouldn't normally go.
If your water isn't hot enough, or your DW does not have a pre-heat setting (or it's turned off), it can leave residue in the cabinet. If there's a bit of plastic or something caught in the drain, it may not drain fully, or could trap some crud there that can't get past it. DW often like water at least 130-degrees, which is often hotter than your supply.