>This should still mean there's an improvement over what would happen otherwise.

Yes, but in this case it most likely means prices would be going up even more without that construction. So new construction helps, but it's not going to slow rent increases much.

>However, if a person did want to push faster creation of new housing as a solution to housing affordability, preventing price fixing is a definite pre-requisite to that working as a solution.

Increasing new housing is the solution to price fixing. The more landlords in the market, and the more options available, the harder it is to control supply.