The idea that property tax is passed down to renters 1:1 is just something you made up.
The concept you need to look into is called tax incidence: https://www.maxwell.syr.edu/uploadedFiles/cpr/efap/Notes%20o...
1. Property owners make a lot of money and own a lot of property.
2. When you increase property taxes, people who own a lot of property pay a majority of that increase.
3. Rent prices don't immediately increase 1:1 when property taxes rise, based on one data set.
Basically, property taxes are mostly paid by people who own property. Most property is lived in by the owner. So property taxes aren't regressive, since rich people end up paying the majority share.
People have been trying to create a model for the impact of rent shifting since the 60s. No one has a good model yet. It's hard to model.
If I sign a lease for 2000/mo, and the state increases property tax on the owner, the owner can't immediately increase my rent. Rents increases are generally governed by local laws. But over time, they can raise it, and it can be reset when the current occupants leave.
So an owner's profit margin takes a hit when property taxes rise, and renters bare a smaller percent of the burden of the new tax than the absolute amount raised in the short term. Long term, renter's are still covering the owner's total cost of that property, otherwise the owner would be losing money on the property – which, if that were prevalent business practice, we wouldn't have that many landlords.
So yes, renter's pay property tax.
But, definitionally your rent must cover the mortgage and property tax of the property you occupy, plus profit. If you rent is less than property tax and mortgage, the land lord is underwater and will soon sell to someone else who will charge more or evict you for remodeling.
In the current situation, when the realty appreciates at >10% per year (in Austin, at least) it's not a very smart decision to sell or renovate the house if you cannot find a tenant willing to cover all your expenses.
For example: Zillow shows my house appreciating 10K per month, my mortgage+tax+insurance is 3K, assuming Zillow is in the right ballpark, it makes sense for me to keep the house even if I can't find tenants for 3K (similar houses in the area used to rent for 2K-3K last time I've checked).
Under less insane circumstances, a land lord who is charging less for rent than the house costs to own is going broke. As a general rule most land lords rent to make a profit, and therefore won’t charge rent below the cost of ownership.
0 - A poorly capitalized land lord will still go broke in this circumstance, since they’ll eventually fail to pay their mortgage without refinancing.