Food also enjoys massive amounts of competition amongst what type of food to eat. Housing doesn’t.
You're actually on to something here. There is far far far more food produced than we could ever consume; so much that a massive amount is literally thrown away. Whereas with housing, we've been grossly underbuilding for decades now. If, in a year, you have 25,000 people who want to move to your city, but you've only added 2000 units of housing, then the inevitable result is that the richest 2000 people get the housing, and the owners of that housing can charge extremely high prices. Given this, why the hell is it literally illegal in most of the land in our cities to build anything other than a detached single family home that might house four or five people, as opposed to a duplex or small apartment building that could house two or three times as many?
I'm not saying that we shouldn't tweak around with the allocation incentives, but there's simply no where to policy your way around the fact that our urban areas have far too little housing for the amount of people who want to live there.