The article isn't great but your analysis is probably worse.

No per Capita analysis? No income analysis? Only two cities?

This is actually a challenging question to answer. Thankfully other people have done research and we can reference that if we actually want to know the answer, rather than just prove our priors to ourselves.

Land is going to be expensive in popular areas, but dense housing means that you can get a lot more housing on the same land, so you can still contain prices, even if they're probably not going to be super low.

Let's look at the prices in Chicago, which is a pretty dense place: https://www.realtor.com/realestateandhomes-search/Chicago_IL... - $350K

Now let's look at the fairly bland, suburban college town where I grew up, which is not dense: https://www.realtor.com/realestateandhomes-search/Eugene_OR/... - $495K!

Eugene is far more expensive than the dense place with a lot of amenities and jobs.

I would argue Eugene’s market is heavily influenced by Nike and UOregon (and recently remote worker flight from downtown Portland) and as such, drawing a line directly from its lack of density to lack of affordability strains credulity for me.

This relationship between density and cost reverses for nearby towns like Springfield even though they share many of Eugene’s characteristics.

The point was that density doesn't "cause" housing to be expensive.

Chicago doesn't have an urban growth boundary.

> I find this article to be embarrassingly bad. Just find metro areas and compare neighborhoods and observe density levels, and see the effect on price.

This sketch of an analysis is significantly worse than what's in the article. You can't estimate effects by correlating levels. You need to correlate deltas, at minimum. You also need a reason to think those deltas are causally linked, in that you're not suffering from omitted variable bias, which is why you need a natural experiment. The article follows this correct methodology by discussing the Austin natural experiment.