So Bob sees your tax, looks at the Ahmed family renting his unit. Says "oh crap, uh, Ahmeds, you're out, I need to put my brother Doug in there to dodge this tax!"
Result: Brother Doug moves from a tiny apartment to living in Bob's house.
The Ahmeds cannot find another place, because half the Bobs are doing a similar scam, and the other half the Bobs are doubling their rents because they can see they now have a good that's in even shorter supply and they don't feel guilty at all for this because they're now paying triple property tax.
The Ahmeds now live in their car and eat cat food.
You know when the number of rentable units goes down, rental prices go up, right? I'm all for going after people who leave units vacant, and for taxing the income people get from these investments, but taxing rental units means making the rent price worse.