I disagree that you can't do this in the US. Considering the UES in New York, just as an example, studio apartments are certainly cheaper than 1 bedroom apartments, which are cheaper than 2 bedroom apartments. Several people splitting a 2 bedroom living space will work out to be cheaper than a studio per person as well.

Also, the US is a big place with different local laws. Be careful about generalizing something across the whole country, because after a few Google searches, I couldn't find any Federal Laws about this.