The problem is land has gotten expensive, not so much construction. Also, regulations and the like generally raise the bar for what is considered an acceptable house, which also contributes to rising prices (eg. things like mandatory minimum parking, housing amenities, etc.

Some places want to ban apartments smaller than a particular size because they are "expensive dog-boxes", which rather misses the point. I imagine the logic is that larger apartments will be available for the same price if such comes to pass... People are capable of impressive mental gymnastics.

Your third paragraph starts to align with what I said. But "buy a smaller house" is not a helpful response to "there are no small houses for sale".

Not if no one is building (or selling) the smaller houses, possibly because of the reasons you give in your second paragraph.