While a good idea, a lot more than zoning needs to be fixed.
Fire codes requiring two stairways have the unintended effect of making 4 bedroom apartments impossible to build and so in turn push anyone who wants just a little more space to single family houses. Those same fire codes have prevented a lot of deaths, and I've never seen a property study on if we can really get rid of them (everyone proposing it points to other countries without those code having lower fire deaths - but they are comparing overall rates including old buildings and lots of different construction styles - so I'm not sure if it something we can safely get rid of in the US context)
If we don't also build great mass transit traffic will get worse - sprawl is a solution to heavy traffic (not a great solution but it is one).
Most places in the US with high density are friendly to specific life styles. They have great bar scenes, theater, live music, arts (and others), but there are lots of other things they do poorly. Importantly the parts with high density are very unfriendly to families and so a lot of people who live in high density in their early 20s feel forced to move to the suburbs in their 30s as they settle down - better schools, parks and other things you want to do with a family become important (these are things that other countries do well in high density but not the US)
On the transit and lifestyle aspects - I think those actually come naturally if you allow the density. And I say that is someone who was an organizer for transit for a decade in Seattle. It would have happened on its own, and probably better, if we did the development first.
