There is at least some truth to induced demand with new housing driving an influx of new residents, especially in cities with economic opportunity.
Just like transportation induced demand, the solution is different style of infrastructure. High capacity metros, bus lanes, and regional rail to get people out of cars and use limited transportation corridors more efficiently than single occupancy vehicles. One more lane bro doesn’t work, but adding new forms of more efficient transportation does.
New, denser housing with mid rise and high rise buildings and a mixture of unit sizes in walkable neighbourhoods with good transit access absorbs new residents and drives down housing costs for everyone. Single family sprawl doesn’t work, but density can.
We have under-built for decades, so it’s easy to misunderstand the signals. More housing gets built and prices still go up, and many people are concluding more housing just increases prices, leading to people with good intentions decrying “luxury housing”. There are plenty of nimby actors in the mix too, tossing in all sorts of misinformation and bad faith arguments, muddying the water.
The reality is areas with strong economic growth are all failing to add enough new housing and demand continues to outstrip supply, leading to higher prices. Many studies have shown even new high end housing helps manage prices, as someone rich enough upgrades, leaving their unit empty for someone else to upgrade into. That chain continues all the way down into the lower cost units, each time freeing up space someone else can afford. Large migration into a region can mess with how much prices can be affected, but studies still show even high priced new units do slow down growth in prices. Supply and demand does apply, we have just massively underestimated how far behind supply is for the demand and need to add so much more housing.