Renters already are paying a piece of the property tax. It's built into the rent. They just can't deduct it.
In general, I'm not sure how great it is that we favor home ownership over renting in our tax policy. My bigger issue is being able to deduct mortgage interest but not rent. Mortgage interest is essentially rent on money, so I've always thought it'd be fair to make rent (or a percentage of it at least) deductible as well. Or, even better, eliminate the mortgage interest deduction entirely.
Full disclosure, I'm a homeowner. Fuller disclosure, my home is paid off, so it's easy for me to say these deductions shouldn't exist. I would gladly give up the property tax deduction if that additional revenue was used for something other than cutting taxes for the wealthy, though.
However if a landlord is like a business owner, and property tax is a business expense, why should they not be allowed to deduct it (just like any other business expense)?
Amazon has expenses too related to storing products in warehouses, which they can deduct. Part of that cost is priced into the product. So in theory, customers should be able to deduct a portion of every product they buy from Amazon?
We built a broad middle class by favoring home ownership, allowing regular folks to build wealth in the form of their primary residence. I think we need to get back to that, and that does mean making policy decisions that eats into the margins of landlords.
Sometimes that's true, sometimes it isn't. Sometimes people wind up with underwater mortgages, rather than building wealth.
I would favor eliminating all business deductions, combined with lowering the tax rate enough to make the change revenue neutral.