I know this is an old thread, but relevant. I am currently looking into a cold water supply dishwasher, for some reasons Joe B stated above...
I not only have a tankless, but it is at the opposite end of the house from the dishwasher. The current dishwasher is meant to be hooked up to approx 120F hot water line (our tankless is set to 140F), but there is no way the tankless will ever deliver even warm water by the time the dishwasher is done filling. So we waste a lot of time AND a lot of water (am in California where water is scarce due to drought) bringing hot water to the sink not only for the first fill, but for EVERY fill in the cycle.
I had read that Bosch can use cold water line. I called, and while that is true it is not recommended for any loads except lightly soiled dishes. According to Bosch, the dishwasher cannot reach full performance from cold.
I also read Miele dishwashers can use cold. I currently have email out to Miele, to see to see what they say.
One alternative is to hire an electrician to wire a new dedicated circuit for an instant hot water tank (or tankless) under the kitchen sink. I'd rather not go this route, I have experience with doing this, it seems they often develop leaks and frequently need replaced every 3-5 years with hard water (mine is moderately hard). I'm retired and am trying to have less maintenance to perform in my home, not more, so would rather not go this route if I don't have to. But it's not practical to keep wasting water and time to deal with a dishwasher that needs a hot line hookup.
If anyone can recommend any other dishwashers besides Bosch and Miele that are known to perform well with cold water supply, please let me know so I can look into those. Thank you.