Earlier quoted context omitted.
There is a sense in which a non-trivial chunk of those productivity gains are eaten up by rent-seeking (in SF/NY, the high rents are literally rent-seeking in that they're the result of deliberate manipulation of local laws & regulations around housing & zoning for the benefit of existing homeowners). Even there, though, a single person can live quite nicely on 100k USD (or 120k USD, if going from 100k Euro), if they…
You were comparing apples and oranges in living standards. The moment you inserted roommates, it became apples and bananas. By the time you will reach public transport, safety etc - it will be apples and cookies.
If you want to raise a family in SF proper, I agree that 100k/yr total income would be insufficient for what most people consider a reasonable QoL, even if one spouse stayed at home to take care of the children to avoid childcare costs.
Of course, in SF, 100k/yr is "entry-level engineer at an early stage startup" territory in terms of earnings, which is not the typical profile of someone trying to raise children. You'd have to be trying really hard to not make double that as a mid-level engineer in the Bay, though.
Keep in mind that even once you get past the flashy comp numbers at FAANG, there are a huge number of publicly-traded tech companies in the Bay which pay enough that you could afford a mortgage to buy a house in SF on a single engineer's earnings without breaking 35% of post-tax take home pay. (A bit of a stretch at 200k, easy at 250k.) Even startups are getting there: a friend of mine recently got a new job in the Bay (not in SF, but close) paying over 200k in cash comp (base + bonus) with less than 5 years of experience, plus some options (which are probably not worthless, but can't immediately be used to pay a mortgage). He's a good engineer but this isn't an unusual outcome; some of the engineers I know aren't as good, but they make more money because they took the interview grind seriously and went for companies with publicly-traded stock.