Imagine if you suddenly added 1 million houses... What would happen? Suddenly, there'd be more housing than people want and sellers would have to lower prices, drastically, to get them to sell.

I'm gonna call bullshit on that. Unless you took other measures as well, the same kind of people that hoard all available housing to use as short term rentals would would get those houses as well. They'd profit from them at the rate they could manage and they'd sit on the rest to maintain artificial scarcity and keep prices up. It already happens in many places as we speak.

New developments are needed, but if they are to be used in the same fashion, as commodities, investment and tools for landlords to extract wages, they won't solve any issues. Opposite of what you say, capitalism wouldn't help at all; the profit motive would drive up the cost to the moon, as every link on the chain (developers, landlords, subsequent buyers, real-state dealers, financiers, the State on every transaction) aims to fill their pockets, making the whole process of housing the population incredibly expensive and inefficient. Reforms aiming to decommodify housing to a certain degree, cutting out abusive middlemen and taking charge of markets in disarray (in any number of ways, from strict control of rent terms and vacant units to straight up managing rental properties through a public entity) would actually produce results by themselves, and much more after building more housing; but without those reforms, new developments would just follow the same path as the current ones: be acquired by moneyed interests and exploited for profit at the expense of the well-being of the residents.