Do your dishwashers not have different temperature programs? Tap water is generally set at 65ºC here. My dishwasher has a 45ºC program, a 50ºC program, etc. Depending on how dirty your dishes are you can use lower-temp program to save energy. They even make dishwasher pods specifically for lower temperatures. If it always takes in hot water it would need a way to cool it down.

Much the same reason as electric kettles not being as popular in low-voltage countries as in Europe - with higher domestic voltage, the appliance itself can heat the water it uses in a timely manner.

We have 230VAC (on all outlets) instead of your guys' puny 120V, so our dishwashers aren't handicapped out of the box and can heat their own water properly. I feel like having to run the tap before doing dishes is an L for the US, not Germany/Europe?

A lot of houses are older than the concept of central heating or running warm water, so there are some homes that don't have central warm water, but instead small heaters under the kitchen sink/next to the bathroom, which might or might not hook up to dishwashers