I’d be fine with all rental housing being entirely owned and controlled by a government body.

Housing is already controlled by a government body, both implicitly and explicitly. The only thing that holds up the housing situation as we know it is that government body – our collective willingness to recognize and abide by it. If we don't like it, we can change it on a whim. We are the government.

Why should where I get shelter from be a market exactly?

That's the question. Why not pick a house you like and move in, its owner be damned? The answer, I'm sure, is because you know the government will soon come and kick you out. By brutal force, if need be.

It takes people like you and me to bring that force. We are the government. If we don't like housing being a market, why are we bringing the force? It's certainly easier to do nothing.

the people we’re complaining to would have some incentive to give a fuck about us.

Why not complain to them now, then?