Housing grants don't make houses more affordable. If you announce to the world that everyone buying (or building) a house is going to get an extra $10000, the prices will go up in proportion, meaning those people will out of pocket the same amount as before. The extra cash will go straight to the seller, on top of the original price. It makes more sense, then, to limit payouts by the type of buyer, because not everyone will be a first home owner, or below a certain income threshold. Limiting payouts to certain types of homes, such as new houses, on the other hand, will raise prices for that type of property across the board.
Mokalus of Borg
PS - It may seem to help on the surface.
PPS - On the whole, though, the money never goes where it's meant to.