I can tell you that all the people that have moved into my East Bay neighborhood with good schools have been from SF. People with kids that can't handle the price for private schools and deal with the kid unfriendly nature of SF.
People -- particularly in the middle class -- moving from core cities to suburbs to raise children is hardly a new phenomenon, and hardly restricted to San Francisco.
Its really the lottery system for the public schools that is the reason most of my friends with kids left SF. People buy houses in certain neighborhoods to guarantee which school their kids attend. Without that guarantee, there is not much incentive to live there.
You mean the broken needles in the gutters, the people taking dumps on the sidewalk in broad daylight, hustlers trying to sell you crack and meth on every corner downtown, and the general ambient smell of piss?