Yeah, last thing I look forward to doing while on vacation is washing my own underwear in a bathroom sink. Just bring the extra pairs--they weigh nothing.
IDK about nomading, but when dirtbagging you have an excess of time. If the sun is down then your day is done. In the winter especially, having chores to do is welcome reprieve from the cold and boredom. And bathrooms or laundromats are so awesome. Warm and dry and bright.
In my experience campsite bathrooms tend to be cold and wet. Bright, sure, but not a place I'd like to spend any time more than needed in. :D
Gotta find a walmart or especially target. They're saunas :)