This is a policy choice, and I would argue it's a bad choice. If we strive to make housing cheaper across the board, households will have more money available to save and invest by other means.
In particular, the incentives created by housing as an appreciating investment are awful. Owners who have all their money locked up in home equity are incentivized to oppose new development, creating an artificial housing shortage.
As a counterexample, consider Germany: virtually all households rent, housing stock is plentiful and affordable, and the middle class is still able to save and build wealth.
That aside, I'm not convinced that encouraging home ownership is bad policy. Home ownership is a direct personal investment in your community, a means of securing one's most base human needs. If people are not building equity in their own homes, someone else is — why is that a superior outcome?
I'm all but certain that's not true. Virtually all non-single-family new construction is aimed at condo sales. Rentals are what you do with depreciating units, not stuff you just built.
I'd look to Tokyo for an example of where it has worked.
Is there an example of this policy direction working elsewhere?
Is the goal solely improving housing affordability in locations with high-demand?
Is exacerbating the wealth gap of concern? Density is almost always developed as rental units; growing the permanent rental class means eliminating access to the only vehicle for building wealth for middle and low income Americans.