They wouldn't build 1 million apartments, for one, Apartments would likely be built at a slower rate than people moving there. Two, as seen in Seattle, only housing for the already wealthy is built. There is tons of demand for low income housing, but no supply because it doesn't make as much profit (if any) so there's no incentive for capitalists to house low income people and the cycle keeps going.

Before I moved into my current place, I was in low income HUD subsidized housing. It was a brand new building with rent control. Rent control worked great, but the owners didn't keep their side of the promise. Maintenance took months, all amenities we paid for were broken, access to the garage to store our vehicles was broken for 4+ months, elevators were broken for months at a time.

There is no way to get people to freely build affordable housing in or around larger cities under this current system.