Property taxes also punish retired people. When your wages disappear after retirement, it's a lot more difficult to pay the taxes on your home.
My parents were immigrants and not savvy enough to buy a house. I'm wondering how I can ever afford a 200K down payment on a million dollar house, and if that is in any way a reasonable idea. Taxing income is the wrong approach since people getting income are contributing to society. The lottery winners who happened to own houses in the right place .. I'm not sure what they contributed.
If you can't afford to save, you can't afford the mortgage.
If they do, then someone who's going to get that house should foot the taxes.