It would do nothing to rents or mortgages intrinsically but it would cause property prices to fall and it could add to the tax burden of regular property owners depending on how it were implemented (i.e. if the tax free threshold were set too low).
>that still wouldn't be much of a disincentive to the wealthy
It would be a massive disincentive to the wealthy, since they own the most property and are used to it being an asset not a liability.
They would dispose of properties that were nonperforming because taxes > capital appreciation + rent and this would spiral as falling prices leads to more hoarded properties being given up.
They would also scramble to rent out previously unrented properties where capital appreciation wasnt covering taxes. More rentals on the market means even lower rents which makes their properties worth even less to them.