IMO capital gains taxes are bad as well, they discourage efficient investment allocation (you are stuck with what you have now).
It would be better if we mainly taxed consumption directly. If you are a billionaire but spend $100k/yr I am fine with you paying the same taxes as anyone else spending $100k/yr.
Taxing consumption hurts people more at the lower end of the income scale than at the higher end. It all comes down to what reserves you have to accommodate different scales of financial events. For example, will not having enough money for a tank of gas break you, or just annoy you? Could you survive needing an ambulance ride? Do copays keep you from seeing the doctor, or are they just a rounding error on your income?
I believe that taxing people proportionally on income earned by labor is a unifying element of a social contract. i.e., we are all contributing to the common good. Income from capital is "free money." You didn't work for it; you took it from somebody else in the form of interest, dividends, or some other rent-seeking financial magic.
At some point, wealth becomes corrosive to society. People acquire it just for the sake of acquiring more and building their personal power. It seems that wealth is used to build more mechanisms of rent-seeking to further extract money from people who make their money through labor.
That kind of non-beneficial use of wealth, rent-seeking, and financial magic should be the target of any tax system before taxing money earned by labor.