We need a multi pronged approach. Basically any policy that improves housing affordability without too much negative or perverse incentive elsewhere should be favored.
And increasing density only works up to a point. Once you can no longer increase density, the prices start climbing back up.
I think rezoning for more mixed use neighborhoods is a good idea, and some high-density living is good (not everyone has kids, or wants to have them) but I am skeptical of increasing density in general.
searching for an answer i found this:
https://nycdatascience.com/blog/student-works/data-study-on-...
which observes that crime increases up to a density of 500 people per square mile, but then decreases as the population density increases further.