Sorry, but your post is riddled with errors. Renters pay the property tax - all of it - of owns.

Nor do higher-valued homes actually pay proportionately more property tax than others. They pay more, but not proportionately more as they actually should.

As for luck, reasonable people would say that it is those who luck out in lotteries and property value increases who should be paying tax, rather than hitting those who have to work to live harder.

Fair is fair.