Rent does not go up because your landlord has to compete with a landlord one town over where the tax didn't go up and so if your rent goes up you will just move.
Your landlord knows moving is a hassle that you'll avoid if it means paying a little more. So he raises it just enough that you won't just pack up the Uhaul and go live there. Then over the next few years, he does the same again, when he can, until he recoups the property tax, or near enough of it.
Some landlords are bad at guessing the correct numbers. Others are savants. In aggregate, renters end up paying almost all of it over time if not immediately, and those that don't end up suffering in other ways (when the landlord just stops paying the tax entirely, but taking your rent, the building gets sold, and you don't get to renew the lease because they're going to knock it down and build luxury condos).
In Singapore and a few other places. However in the US housing is not a government monopoly (sometimes low income housing is). You can always find a landlord in a different town. No need for a new job as you still live in the same metropolitan area.
Ok but what if the landlord raises rent by $200, while commuting would cost me an extra $250. Or what if I move from a town with good public transit to one where I have to drive by your own admission, several towns over.
What if moving costs $1000, which is another $83 per month over a year.
Note that it doesn't need to you personally that moves. Even people who would move anyway will force lower rents just to attract new renters. It takes longer this way but renters typically search a large area when looking for a new place and they care about their costs vs ammentities.
Some landlords are bad at guessing the correct numbers. Others are savants. In aggregate, renters end up paying almost all of it over time if not immediately, and those that don't end up suffering in other ways (when the landlord just stops paying the tax entirely, but taking your rent, the building gets sold, and you don't get to renew the lease because they're going to knock it down and build luxury condos).