So, if there is no such thing as a real "fair tax", my question should be "what would be the fairest tax". I lean towards a national sales tax of some sort.
One recognized consequence of capitalism is its tendency to distribute wealth from some segments of the population to others. The longer it goes on, the richer the rich get, the poorer the poor get. That's the motivational aspects of it.
The most dysfunctional aspect of that is that in most societies wealth confers power and power tilts the playing field. It can become irreversible. And society can become unstable, a consequence that has no winners.
So one aspect of taxes on money, income or wealth, is to undue, to some degree, what capitalism does.
Fair? Depends. Some would say no, but would not like the consequences of not restoring some of what capitalism creates.
The people that capitalism benefits the most give back some of their winnings.
Capitalism's losers, win some back.
Society remains stable.
There is substantial evidence that we aren't doing enough correction these days. Many social ills on the rise these days correlate highly with extreme wealth inequality. We are among the most extreme in our inequity. The top 20% of us possess all but 15% of the wealth.
"Fair" is what works.