I live in a city that is taking active steps to increase its density and affordability (https://minneapolis2040.com/). This directly affects my neighborhood. There are two kinds of construction going on around us. First is higher-density apartments/condos in the 3-5 story range, often with first level retail. These aren't replacing homes, though - they're replacing light industrial like warehouses.
Second, and this is an interesting rebuttal - some of the 100 year old houses are being torn down and replaced with new, larger (and much more expensive) houses on the same lots. So a worn-out 1200sf bungalow on 1/10 acre gets turned into a 3200sf quasi-mcmansion on the same lot. These new houses cost 50-100% more than the old houses in the neighborhood do (more like 100% for the run-down homes they replace). But they are contributing zero to the overall density - they're still single-family dwellings. Even the old two-flats in the neighborhood contribute more density.
So rather than increasing density, they're increasing cost of living. That is your #invisiblehand in play, without NIMBYism stopping anything.
I don't think it's just zoning here. There have been some small multi-family units built. But they don't sell all that well or seem economically attractive to builders.
And back to my point... I think there's a lot of sort of theoretical macroeconomic handwaving going on when it comes to housing density that flatly rejects engaging with real world conditions in any way. It sounds smart, but it's dumb.
That's exactly what needs to change in "make it easier for houses to be built". Make it easier means don't let NIMBYs block housing.