You don't necessarily hurt anyone, you just lower the attractiveness of real estate as an asset class. The yield chasers will move their money into a more attractive asset class, the value investors who buy real estate for price stability or tax reasons would stick around with lower yields.
Yet you'd be helping everybody else who didn't take on irresponsibly large debts.
House prices would go down though - a house with a high recurring tax is much a less attractive investment.
My city has several blocks of its downtown used for surface parking lots. If a lot with a building paid the same tax as the parking lot, how long do you suppose it would take for the parking lots to turn into skyscrapers with parking garages?
Of course, this would also force people to sell their property to pay the tax.
New York and SF could do that tomorrow.
Raising property taxes would also help drag down the prices to saner levels and ensure that this rich source of rent ends up distributed fairly rather than coagulating in the pockets of the 0.01%.