Don't teach them kids to waste water rinsing dishes! The dishwasher works most efficiently if chunks of food are removed (scrape into trash), but not rinsed.
Comparing it to food doesn’t make sense because food has to be planted, watered, fertilized, harvested, and transported. Water that falls into a local reservoir takes a negligible amount of energy by comparison.
Water is abundant is the ocean, but it is not drinking water. Drinking water is a scarce resources and using it to rinse dishes that are going into a dishwasher is an unnecessary waste of a vital resource.
It may be considered safe to use to water your lawn unless it is too acid, but you should not drinking without treating it first. Especially if it has been collected and stored in a reservoir.
Then again food literally grows on trees, you just have to collect it.
Point is most of the time dishwashers do not run on rain water but on drinking water which is a scarce and vital resource so we ought to avoid wasting it.
Technically a nonpotatable unpurified water tap could be used for the same purpose but in addition to the risk of "oops accidentally drank direct river water with pollution and/or hazardous natrual bacteria" the infrastructure for the fringe use would be less efficient than just purifying more water to be flushed down the drain as a cleaning process. Plus in say southern California the freshwater purification is not the limit but the input water hence the dirty looks for bottling it there instead of say the Great Lakes area where it is actually abundant. Hong Kong I believe is one of the few places that uses salt water to flush their toliets despite large seaside cities being in no way rare.
It is like mass production technically wasting more materials - at that point it usually doesn't matter compared to the sheer efficiency gains.
Granted non-sustainable uses of source water is something to be accounted for.