>The City is capable of building housing tho, right? They have outsourced that to private companies via incentives, but they COULD right?

With what money? Neither municipal, nor state nor federal have any. The US at the federal level alone is approaching a trillion dollars in interest payments this year. It's the least productive way to spend money and yet, everyone constantly looks at the administrations to solve problems. Every time they do it, that slice gets bigger.