Hand powered washing machines are useful in a number of situations, most obviously power outages, in which dependence on the laundry machine quickly leads to the downfall of civilization altogether.
But they're also quite useful in small apartments, dorms, or maybe a cabin, particularly when only a few items of clothing need to be washed at a time. Athletic clothing in particular is a great reason to use a hand powered washing machine, since you might only need to clean one outfit at a time, and it would be extremely inconvenient to wait until a full load of laundry is ready, or use a full-size washer only on one or two outfits.
Other great uses include RV camping, children's summer camps, base camps on hiking trips, road trips with little or no access to laundry facilities, and plenty of other situations.
Not to mention the simple fact that it is electricity-free, and plenty of people get a sense of satisfaction managing their own affairs without having to plug into the grid.