It's a drop in the bucket compared to what's needed, so I think the solution needs to be mostly market-based, but it's going to take a lot of different approaches to fix things.
Everybody wants to live in NYC/SF/LA/London/Paris/Tokyo/...
The moment rents drop for whatever reason (more building), a new batch of people will finally afford to move in.
And people say everyone wants to live here in Bend, Oregon.
And people say everyone wants to live in Boulder, Colorado.
Just maybe... it's not actually true.
And Tokyo, by the way, does a pretty good job with housing: https://www.vox.com/2016/8/8/12390048/san-francisco-housing-...
Only in the sense of getting more bang for the buck. It's the 10th most expensive city to rent in the world: https://infogram.com/1prdmkx1zvdve1sg79z2vp56vmsm2ygmn90
Or a more comprehensive study here: https://www.dbresearch.com/PROD/RPS_EN-PROD/PROD000000000049...
Notice something in these list? It's all famous cities. The fact that they have wildly different housing regulations doesn't affect the rent prices, any supply is immediately absorbed back.
https://www.sacbee.com/news/california/article208678414.html
They want removal of regulation regarding parking spots (free market), but building of rent-controlled social housing on the freed space (non-free market).