You're totally right. It would be better for home owners since high houses prices make everything about buying and selling houses more expensive. You can't realise your housing gains except by dying. Or downsizing, but many old people rattle around in 3+ bedroom houses until they die or are forced to go into a retirement home.

It would also involve building more houses, which is bitterly and loudly opposed by a subset of home owners. Home owners are also richer, older, and vote much more than the (generally) poorer, younger renters.