Off topic: How much time people spend in public laundry? In post Soviet countries and Russia almost all families, even poorest have washing machines, while public laundry used only for complex cleaning.
A functional, used washer can be had for $100 in most places, which shouldn't be a huge barrier to most people (especially people who can afford a videogame console). Small apartments don't have washers because they simply don't have the room.
Definitely some weird cultural thing that people rent flats without them. You wouldn't be able to do that in the UK.