It only leads to housing prices rising (in the long-term), if NIMBY politics makes building new housing essentially illegal. There are plenty of examples of "boom towns" throughout history where prices may have rose initially, but didn't spiral out of control, and usually settled back to a reasonable baseline relative to wages.
We aren’t at the root cause yet. NIMBY politics are largely caused by the idea that housing is an investment rather a basic human need and depreciating asset which is a rather new idea in relation to “throughout history”. People generally don’t want to vote for things that harm their investments and building new housing harms the investment that all current homeowners have made.
If society thought of housing similarly to other large purchases like cars in that there was no expectation of profit, we would all be a lot better off.
Now what caused this housing as investment idea? I haven’t seen any research on this, but my guess would be as a form of forced retirement savings as it allows people to build net worth without the self-control normally required of saving. And the difficulty of that delayed gratification is really just human nature.
It's also the easiest way for most people to achieve high leverage. My friend got a $3000 down home loan in Colorado. $3k in for $450k. The leverage on that is astronomical. A 10% appreciation in value gives him 1500% growth in wealth, with no capital gains tax when realizing.
FWIW Calgary, AB is an example of tons of building doing a good job to manage housing cost increases. Something like tripled the population ~300k -> > 1M over 1990-2010s and house prices remained reasonable in the suburbs (which are still Calgary proper). One thing Calgary did well was "Infills" which basically was when someone would split their single family home into 2 properties, which may or may not share a wall. Sometimes they'd buy neighboring properties and do N parcels to N+1 (or >N) new homes. eg 2 neighboring parcels became 3 homes. Smoothly incrementing the density.