Policy restricting housing is indeed another factor impeding housing. The price controls I'm referring to are rent controls (which applies to ~70% of apartments in SF, and the threat of reintroducing rent controls looms) and affordable housing mandates. The affordable housing mandates require that a certain percentage of units are rented at set prices.
Again, if housing isn't an investment opportunity, then why would anyone build new housing? Sometimes people get together and build co-ops. But those are rare, and it's only available to people with a lot of capital on-hand. Plus, it runs the risk of the project going over-budget.