Land is a rivalrous good but housing isn't. Sprawl is just the most conflict free way of giving everyone what they want but it's not the only way. You can always build more housing on the same piece of land.
Supply and demand is pretty obvious because of the basic physics behind it. If you have a world with 10 houses and 20 people then 10 people will be without a house. It's not very difficult to see the problem and how to respond to it. We first have to establish that we want every human in our country to have shelter. That means what we don't want to happen is the allocation of housing to a subset of the population, be it via the free market, a lottery or an application process where you are vetted by an interviewer according to some criteria. We don't want any of that. So the obvious solution is to just build more housing, regardless of the economics.
Now lets just add a thin layer of economics.
It turns out that the free market has this interesting property that in the case of demand exceeding the supply the cost of housing increases until it becomes profitable to build more housing. It's a self balancing system if you make sure that it's not getting stuck somewhere.
Turns out if you make it really difficult to build more housing then people decide to pack up and leave because that's the only option left. For the sake of the argument 20 people can't live in 10 houses so 10 people will have to go build housing somewhere else.
Now here is the perverse thing. The same people who made it difficult to build more housing also made it so that they get to stay where they are by removing the pressure to leave the location. What we get is 10 people living in housing and 10 people living in misery. You don't need an economic resource allocation mechanism like the free market to cause misery. The misery already exists in the real world and the economics merely summarizes that misery as a price signal.
So why care about supply and demand? Because it's the closest thing to physical reality but what people fail to grasp is that you have to change physical reality to change the economics. No, messing around with prices via rent control or prop 13 does not solve the underlying problem.