No, the goal is to make rich go away, and make poor have a place to live where they have more economic opportunities. If you cannot afford to pay $1k/month property tax, it means that you have an asset worth around $1M, so by no means you are poor.
If you cannot pay $1k a month in taxes, you probably cannot rent the place, either. The taxes driving the owners away will drive the renters away, too.
I don't consider anyone with 300k in net worth poor. And the goal is to not subsidize these individuals who have just had a massive windfall, which screws up the rental market leaving the truly poor(renters) SoL.