Usually no more than 80% of total watts (1400w for a 15amp and 1920w for 20amp circuts).
Modern/newer wiring long as it is properly installed might be able to carry >80% loads for along time and repeatedly, but housing stock (and common sense for that matter), in the United States varies.
In NYS for example you still have many, many homes and apartments with fuse boxes and barely 100amp electrical service. Even then it is common to find only a handful of outlets all on the same circut.
So if the washer or another electrical appliance is pulling near or full power, to avoid tripping the circut or blowing a fuse nothing else *should* be running at that time.
Methinks much as with everything else these days, manufacturers build to one set of specs, rather than trying to allow for differences.
Case in point older electric dryers that could be wired for either 220v or 120v have mostly long disappeared, IIRC.
As for heating water in a washing machine, most American sold units probably are working under the design that unlike models sold elsewhere in the world, these units are only going to "boost" cold or warm tap water to hot. This suits the common 120v/15amp or 20amp service found in most domestic settings.
Yes, I know persons go on about how many laundry rooms or such have a "dryer" electrical circut for 220v service, but that is not totally common. Indeed Miele tried for ages to sell Americans washers and dryers using that line of thought, and look where it got them.
Then we must consider cost. For those with acess, natural gas or oil are a much cheaper way to supply energy for heating purposes. Here again this is where the United States differs from say Europe and the UK.
On the other side of the pond coal, wood,peat are pretty much all the natural resources for generating heat. Well aside from oil and natural gas coming out of the North Sea region. Combines to make electrical power the common source for heating, at least as far as laundry and dishwashing appliances are concerned.
Even at rates that would make most Americans cringe, one would wager EU/UK laundry and dishwashing appliances are more efficient because they run on 220V (or in some "old" cases 400v) service.
Long as 120v service remains the common electircal supply in the USA, there are limits to heating capacity.
While it is possible to heat even the puny amounts of water used by most American front loaders on 120v service. It is going to take a very long time. With today's modern detergents the wash will probably be mostly clean long before that unit reaches 120F from 85F. In which case the unit will still leave the heating portion of the cycle and commence with the wash. All the while exposing laundry to un-necessary wear by long wash times.