You can only build multifamily housing in 3% of the city. It's illegal everywhere else. You can't build more than 3 stories in most places - it's illegal. The supreme cost of housing here comes partially from the fact that you can only build a tiny number of units on land that could otherwise hold much more. So you split the cost of land among, say, 5 condos, and not 20. If you're paying 1/5 of the cost of the land and not 1/20 of the cost of the land when you buy your condo, it's obviously much more expensive.
I'm fine with increased density housing in the peninsula. But, this is mainly going to help developers (who are already rich). You'd have to build skyscrapers not multifamily units to address this problem (the area is intensely hot).
Again, my only beef is on the $150K quote from your interview (and your requirements for "walkable to downtown" and "kids can bike on the street"). I think your argument would be much stronger if you backed off on that, and cited a more reasonable compromise (living 30 minutes from PA).
Palo Alto traffic is already really, really dense. Building a lot more housing, even if it's close to downtown/transit, is going to increase traffic tremendously. In addition to building this housing, the city would need to improve its road throughput. This probably would have to include removing the various one-way barriers in the city that currently preclude optimal traffic flow.
Multi-tenant buildings are the key here. Cost of land is inversely proportional to the number of units. Building up, shared outdoor space, etc. all lower cost for owners but are often prohibited by local municipal regulations.