That should work to lower prices but will also increase costs for home owners. If the goal is to increase home ownership rates then giving them an advantage in the market can help.
You could distribute the money raised as either tax cuts to income tax, or just as a flat dividend to every citizen. If a person owns an average house and pays $10k in tax, their dividend would return $10k - so no loss.
If they own 5 average houses and pay $10k per house in tax, they'd pay $50k and their dividend would return $10k, so would have to pay $40k more