It seems like it would be trivial for the machine to pump water in, turn on the heating element, and wait until it reaches optimum temperature before beginning the cycle.
They do in some markets and don't in others. In particular, in USA, regular 110v circuits don't carry enough power for water heating.
This is what most (all?) of machines do. Heat water when they need hot water
My understanding is that energy efficiency requirements prevent this. Dishwashers have a fixed energy budget they are allowed to expend, which may not be enough to heat cold tap water up to the optimal cleaning temp.