Earlier quoted context omitted.
Well, SF runs a lottery system, so your rent was largely irrelevant until recently (the system is changing to give some preference to people who reside in a school district). That said, you really should investigate SF public schools a bit more. There are a large number of very high performing public schools, as well as some terrible ones. That's actually no different from the 'burbs, it's that if you live in the Gun…
Having a large chance to have your kid land in a poor quality school is reason enough not to live someplace. (Unless you can afford private)
So even though I disagree with you that the odds of a bad placement is "large" (I'd say it is non-trivial rather than large, but I don't have numbers either) this process appeals more to poor or middle income people than wealthy ones. If you're poor or middle income, you're choosing between no chance of a good school (you can't afford the top districts in the burbs) and a decent chance (SF). For a rich person, you're choosing between a guarantee (burbs) and a decent change (SF). Again, we disagree about "large".
One thing - have you looked at greatschools.net and checked out the number of elementary schools in SF with high test scores? SFUSD a very high performing urban district. It's fine to disagree, but if you haven't done this yet, I really do urge you to review the data before forming your opinion. I think the notion that SF schools are mainly bad is an incorrect myth. There are problems, but the notion that good elementary schools are few and far between is false.
High schools aren't quite as good, but they aren't nearly as bad as people make them out to be (it's not just Lowell - check out the data. Balboa high, in a relatively low income southern part of SF, scores as high as many reasonably good suburban districts).
Middle schools seem to be the weak link right now, though again, please review the data before forming your opinion - the conventional wisdom is almost always more dire than the reality where it comes to sfusd. Middle school is a tricky one - you may notice that the private model rarely splits out 6-8 grades, going with the k-8 model, so the entire approach may be flawed here...