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.
I haven't seen a single London or Edinburgh flat (which on average will be much smaller than the US ones - even Manhattan) that hasn't had a washing machine in. One of my friends flat was incredibly small but still managed one.
Definitely some weird cultural thing that people rent flats without them. You wouldn't be able to do that in the UK.
