@mikeklondon
Welcome to the board. US dishwashers use hot water fill, but the dishwasher also has a booster heater to raise the temperature above hot water line temp for the final rinse. I believe the final rinse temps on my Bosch DW are something like 150 F for "normal" cycle and about 160 F for "powerscrub plus" cycle. My hot water line is about 135 F, so the machine pauses while the heater kicks in. Yes, the dishwashers run on 120V, but the heater only has to raise the temp by 10-25 F.
That said, where I live, it costs 3-4 times as much to heat with electricity as it does with gas. I have a gas water heater, gas clothes dryer, and gas range cooker, and the monthly gas bill in the months when the house doesn't require heating (e.g. April to October or November) is about $12/month. The bill rises to perhaps $35-40 in the coldest winter months, with all of the increase going to keeping the house warm.
I have a natural gas 40 gallon storage tank heater. Installation of a tankless gas heater system would lower the monthly bill even more, but the cost of installation to retrofit an existing system can run >$1000, so if the gas bill dropped $2-3 a month, how long would it take to recoup the added retrofit costs (the issues are installation of a larger diameter gas supply pipe plus a larger/more durable exhaust vent). In new construction, a tankless system is more likely to be used because then the installation costs are not much more than for a storage tank system. In addition, the cost of gas tank water heaters has been rising due to increased regulatory requirements regarding emissions and ignition (now must be electronic, pezio-type ignition rather than an always-burning pilot light), so that the cost gap between tankless and tank models is shrinking.
Heating DW water from line cold to proper washing temps with electricity would be prohibitively expensive in many parts of the USA. And slow, unless 240V were used. US homes may have 240V outlets in areas such as laundry (for a dryer), water heater, and kitchen (either a range cooker, or built in ovens plus cooktop). However, standard kitchens are normally equipped with only a 120V outlet at the DW position.
My home was built 1988. In the US, new homes will include a DW and either range cooker or built in ovens plus cooktop (these are supplied by the builder; upgrades possible in some cases), and sometimes the option for a built in refrigerator (often, however, they leave a 38 inch gap in the cabinets where you supply your own freestanding fridge, and the space will be plumbed with a water valve for icemaker use).
In my case, the builder supplied a gas range cooker with a 120 V outlet and a gas pipe (the outlet supplies electricity for the range cooker's controls/clock/timer/interior light). There was no 240V outlet option. I guess they assumed that someone upgrading the range in say 8-10 years would simply purchase a better gas range. Convection ranges, initially introduced in the US as 240V electric models, did not yet (1988) exist, so there was no provision for 240V service. One could add 240V but it would have required complete demolition and rebuilding of the cabinets/walls to add the addition circuit lines.
I waited to upgrade until gas convection ranges began to appear on the US market (late 1990s; I bought mine in 2001). That way I could simply ditch the old range and add a new convection range that needed only a gas supply pipe and a 120V outlet.
Re: cleaning ability of hot water fill in a DW---I think it's a different process because what you are washing in a DW is nonporous, so there is nothing to "set" a stain. People who wish to soften baked-on food in a pot or baking dish often soak it in hot soapy water as the first treatment (perhaps to prepare it for hand washing or inclusion in a DW load).
PS beautiful looking dogs!! The newest versions of Frigidaire's (Electrolux) FL washers, with 4.4 cubic foot capacity, include a "pet bed" cycle.