I know the Bay Area reasonably well. While there are certainly areas of the Bay Area that are low enough density that you could alleviate price growth somewhat in the short term by changing planning rules, there's nothing about the Bay Area that makes it different to London in this respect. The limitation will remain land prices and congestion, and if you alleviate congestion the demand will quickly clog things up again.

This is overall not a location specific phenomenon anyway; it's a factor of the fact that the construction cost per unit goes up above a certain size because of overhead (e.g. lifts, structural elements and services makes up an increasing proportion of the overall building volume), and that network effects tends to drive up demand to desirable locations when accessibility improves. You simply can not increase density to a particularly high level without driving costs per unit of space up to levels that prevents you from cutting prices much. The inflection point changes over time, but not particularly fast.

This means that any area that is already relatively high density, like the Bay Area, faces a rapidly diminishing return on investment in trying to increase density.

Now consider the vast amount of pent up demand in this region, and you can increase supply dramatically without much impact on prices.