Hong Kong is super dense and super expensive, Shanghai is similar, but at Mainland Chinese prices. I'm all for density, but anyone who thinks that density alone solves affordability issues simply hasn't travel enough.

Density is a way to deal with expensive housing. Not a cause of it.

Density is a way to make cities more livable and attractive, and to scale up public transit investments.

After you've done all this, you'll find that your city is more expensive than the surrounding cities without, not less.