I’m so confused. Whose dishwashers are you talking about? I’m in the US, you’re describing every dishwasher I’ve ever had, except that we always hook it up to the hot water line. Our unit takes very little water, it takes hours to run a load due to efficiency features. It has a heating element inside to take whatever water it gets and keep it hot for the cycle.

I don’t really see why it’s any less efficient to use the hot water we are already heating with our water heater (which heats much more efficiently than a small electric heater would). The water originally arrives to my house cold, it has to be heated one way or another. My dishwasher is less than 10 feet away from my water heater, water is not losing appreciable heat on the way to the dishwasher.