So like a love hotel (http://en.wikipedia.org/wiki/Love_hotel), but sans coupling. Or like a capsule hotel (http://en.wikipedia.org/wiki/Capsule_hotel), but with attached shower.
Even on non-prime real-estate (which does that exist in SF?), I don't think you could hit your $20 price point with the amount of housekeeping needed for a bed and shower. Even if you could, after a week your staff might hate you. :-)