> dense towns/cities will always be more affordable

In my experience, that isn't true. At the very least, it depends on what your preferences are. If I moved my home from outside Austin to inside the city, I couldn't afford it.

Densifying a city will make it cheaper than if we don't densify, but we usually densify because of high prices, so high density correlates with high prices despite being a counter-force against it.

And, yeah, living in a dense city definitely tends to cost more than the suburbs, especially per-square-foot. There might be exceptions (high crime urban areas with wealthy suburbs), but you're usually getting a pretty nice house in that suburb.