I could be wrong but I'm pretty sure that even today almost all US dishwashers have some mechanism to heat the water, just maybe not the giant exposed element in the bottom like older ones. Water out of the tap is going to be on the low end of usable dish-washing temps at the very beginning of a cycle, let alone 45+ minutes later.

The reason cold or luke-warm water is a problem is that the programs are extremely simple and just assume the input is 110-120f and won't stall the cycle for waiting for the target temp.

I forgot about the exposed element. These days most plastic spatulas withstand high temperature. Back in the day I think every North American family had at least one yellow spatula destroyed by the element.