And which one makes sense to do as costs go up… property taxes fund things. If you build a $100,000 home it’s hard to charge $8,000/year in property taxes on it.
That's true. However, if you build a $5 million apartment building with 15 apartments on 2 or 3 lots (or even just one) the same size as that $100,000 house, you could charge significantly more and it would be perfectly viable.
What's more, you could house 15-20 times more people.
And the places[0] where a whole house costs $100,000 aren't the places we're talking about.
And those places certainly aren't the ones where increasing the density of housing will do much good.
Note the distribution of median house prices in the site I linked. The really expensive places are clustered around densely populated urban areas (and ski resorts in Colorado).
Increasing housing density to match the population density makes a lot of sense there.
Longer term (as I mentioned in another comment[1]), building out infrastructure and housing of all types in poorer, low population density areas can make them more desirable and provide an economic boost, while taking pressure off more densely populated areas.
[0] https://www.nar.realtor/research-and-statistics/housing-stat...
I suspect the appetite for suburban living would dry up if we all paid the actual maintenance costs of those streets, water and schools on a land-value basis