When I researched this I couldn't find any strong evidence suggesting that more building would lead to more affordable housing.
You would think that more construction would lead to more affordable housing, but it seems like more construction doesn't just increase supply, it also increases demand, which can offset any price effects from the increase in supply.
This makes sense when you think that similar people want to live in proximity to people like themselves. So if there are more luxury condos in an area that's going to create demand for more high-end retail, which will enhance that neighborhood's appeals to wealthier customers which will then increase demand for more luxury residences.
Vienna and Singapore seems to be cities that have overcome this trend.
So I used to be an enthusiastic YIMBY, but there just doesn't appear to be any concrete evidence that more construction is going to lead to more affordable housing.
Having said that, I do believe we should promote more construction, I just don't think it's going to reduce the cost of living to a sustainable level.