Does building where the prices are highest always reduce average commute times?

It's late and I don't have time to do this justice, but I do want to take a minute and get it in the housing thread, because it concerns a claim that shows up a lot, implicitly and explicitly. 

Before the housing crisis reached a boil, the main argument offered by the NYT/Vox YIMBYs was based on the carbon footprint of people driving long distances to their jobs. We might push back on their estimates of the impact of the commuting (particularly in an age of remote work) compared to other green policy changes, but there's no question that having fewer cars on the road driving less would be an environmental win. Nor is there any question that far too many people are forced to make horrifying commutes because they can't find affordable housing closer to major employment centers. 

But can we go further and treat housing choice as a simple, straightforward trade-off between commuting distance and affordability? Probably not. There's quite a bit of research around this question that I hopefully will have time to get into later, but for now I've got some interesting counter-examples that are especially relevant to our ongoing discussion. 

From the American Community Survey, here are commute times for those who do not work from home. [quick caveat, I'm not familiar with ACS data so it's possible I'm missing something]:

Keep in mind that SF isn't very big and SM is tiny (with a reverse commute). Driving over twenty minutes from anywhere in the latter and more than thirty minutes from anywhere in the former will take you to or through neighborhoods with lower housing costs. If we're looking at a trade-offs between distance and price, this should almost never happen, certainly not the majority of the time.

This isn't hard to understand. SF and SM are tremendously desirable places to live (not my cup of tea, but even I see the appeal). It's not surprising that people are willing to pay more and tolerate slightly longer commutes to live there, but if you accept that this is what's happening, some interesting consequences follow.

Of the people in the Bay Area and LA who would like to live in SF and SM respectively, the vast majority do not work in those cities. If you increase housing capacity in these popular places and hold the desirability constant, we would expect to see acceptable commute times going up. That suggests that some people who had previously considered a forty-five or sixty minute commute a bit too much will change their minds.

And environmentally speaking, that's a really bad outcome.