I stumbled across a 2020 OIA request to NZ Treasury where someone asked:

what analysis Treasury has done on the KiwiSaver First Home scheme affecting house prices, and how much taxpayer money gets transferred into the housing stock

Treasury released a few internal docs and they basically say that increasing caps would lead to higher house prices and that subsidies for renters/buyers tend to be captured by landlords/sellers instead of improving affordability long-term.

The advice was apparently ignored.