The amount of water heated up in each cycle is small enough that 1500W is not the limiting factor. Maytag recommends connecting to the hot water outlet and recommends a minimum temperature of 120F [1].
The Miele user manual for their USA models recommends connecting to the cold water inlet unless the hot water is known to be heated by a very efficient source [2].
It doesn’t. They just assume that the user is looking for the most efficient solution. There are pros and cons though. The delicate crystal cycle uses a very low temperature and will only work with cold water. Some of the faster cycles will only be as fast as claimed if the supplier water is already hot.
Huh? How does it matter to the dishwasher?