I don't follow. If you make holding an investment property more expensive than owning, than fewer people will own investment properties, reducing supply and increasing rental prices.

Yes, the investor makes less, but the expected result is less supply so rents are higher, not the same supply but with strictly lower rents.

Renting homes and building and selling homes are two different business.

Higherand higher marginal property taxes for owners of non primary residences disincentivizes owning secondary residences, hence disincentivizes renting, hence decreasing supply of buyers wanting to buy homes.

There will still be first time buyers or people moving, so builders should still have incentivize to build homes, hence supply should not cease to come online just because there are fewer landlords.