> Without Prop 13, a big chunk of the NIMBYs who are currently against more housing would likely change their tune if they had to choose between no new housing or much higher property taxe

I mean, the way you make housing units more affordable is to make more of them, but for existing homeowners of SFH, building condo buildings in their neighborhood will increase their property value because the competition for the remaining lots increase. Given we build close to zero family friendly multi family in this country (ie, appartments buildings have zero family oriented amnenities), there isn’t much in there for nimbys. It’s the right thing to do but you can’t except nimbys to join in on a purely monetary basis.

>appartments buildings have zero family oriented amnenities

This isn't always true. I've seen apartment buildings that have a playground and little astroturf field and some small goals. The kids also are using the pool pretty heavily in every apartment I've lived with one. Some have other facilities like basketball or tennis as well that kids could take up (or use the smooth surface for skating or something).