I would say that they're creating the short supply, and the real issue is that we're able to charge money for something people need to live. That almost always causes exploitation.

Normally when a price for a good/service is too high, we can stop buying until prices go down. With necessities though, if we stop buying, we die. That means landlords and home sellers don't have to adjust prices much.

I feel the solution isn't to make a shit tonne more homes. It's instead to stop charging money for homes. Unfortunately this isn't going to happen willingly.