"The key is increasing supply" assumes the goal of new housing laws should be to increase supply and bring house prices down. But a lot of people do not agree with that goal. Many people are homeowners who will get tens of thousands of dollars richer if there is less supply and prices rise. And in America at least, homeowners have more votes than renters or builders or landlords or the homeless or other groups. So new housing law tends to favor the goals of homeowners, not the goals of other groups who want more supply.
It's more complex than that. When I'm not looking to sell, I certainly don't want the assessed value of my house to increase. That just means, higher property tax bill for me.
Also, houses get older every day. Tastes change - ranch, open-plan, multi-story, multi family get more or less valued as time goes on. Not just 'fewer houses means better resale value'. In fact, a shortage may not change housing prices at all - sometimes it just makes them sell faster.
It's easy to take a complex picture, connect a dot or two and draw a line from someplace to some conclusion. But it's always a trickier picture than that. You gotta consider more dots and connect them all.