The main price driver is speculation, so I'm not confident that increasing supply in anything except for absolutely massive numbers (which 10k/year is not) would have much price impact.
I think speculation is part of the equation, but not the only part. There is also lack of reasonably priced rentals and housing within a reasonable distance from transport infrastructure. Current build out is focused on the high end of the market, or green field sites in the middle of nowhere.
