Why not just tax based on the number of homes, isn’t that a better idea?

If someone owns three £10M mansions, they’re potentially depriving two families of homes but way of scarsity, but frankly if you can afford a £10M mansion is it really an issue, as you’re not being deprived of a home?

If they instead own one £10M mansion and forty £200k flats/terraces, they’re potentially depriving forty families of homes and so should probably be charged twenty times as much to dissuade people from buying up the cheapest homes.