Why would that save energy? It’s going to be resistive heat, which at best matches the water heater. Some models in the US include a heating element, but it’s more of a convenience. The vast majority are simply connected to the hot water line, since that’s why it’s there.

Also, let’s talk numbers. From what I could Google, EU dishwashers use 1-1.5KWh/load, while US dishwashers use an average of 1.15KWh/load. Certainly there are more efficient models, but this shows that there isn’t a significant difference in energy usage between them.

your energy calculations are forgetting the energy cost of the pre-heated water, it’s the appliance equivalent of an offshore tax haven!
Do European homes not have hot water heaters?
They do, they’re just not connected to the dishwasher so don’t need to be factored into its energy usage.