The UK has such small apartments, I guess it's down to how small the country is. I think a lot of American people would have a hard time visiting some apartment buildings here and understanding the small sizes. The apartment I live in right now is one of the largest I could find in my current location (Brighton) and I wasn't being cheap (I'm paying $2500/m) and it's only about 450 square feet[1]. I've found that it's quite literally impossible to get an apartment here at 1k square feet unless the cost is >$10k/m, but in America a lot of people consider 1k square feet to be small.
Here's an interesting chart about average sizes in a couple of different countries, the difference between the UK and the US is huge: http://www.apartmenttherapy.com/average-home-sizes-around-th... (this is houses, but most apartments I've visited in the UK are about the same size as the upstairs of a house, so splitting the figure it half seems a good estimate for apartments)
I would theorise that the majority of people living in small apartments are the sort of people that are young and still finding their path in life (career, education) and so don't spend much time in their apartment (most young people that have their own place don't have the luxury of spending 8 hours a day at home, excluding sleep) so they're not that bothered by living in a small space. It's where they sleep and eat and that's about it. If you're a 40 year old that has a career and family living in 200 square feet would seem insane.
I used to live in 170 square feet (16 square meters) here in Montevideo, Uruguay, under the proposed SF minimum.
It was enough for a single student/worker like I was at the time - though I did wish for slightly more space, 220 square feet sounds like about right.
Over here, there's a boom of construction of "studios", they sell for 40.000 dollars and rent for about 400/month.
One thing I hope is that they don't cave on the need for natural lighting, I had a view to a wall and it was depressing. But overall I think it's very reasonable of SF to allow these.
