Did I say that it would? The 10% was your number. Pick the percent that would hit only millionaires and billionaires, if that is your premise.
You seriously think that paying 20% of income means the same to a single parent (say a widow of a sailor who died fighting Iran) waitress who makes $30K per year as it does to a CEO making $3M per year?
To take your "skin" analogy, 20% for a waitress making 30K would mean six thousand dollars, leaving her with $24K. That's skin, muscle and bone for a woman trying to feed and educate children by herself. 20% for a millionaire making 3M is six hundred thousand dollars, leaving him with $2.4 Million. He'll get by much easier on that, even if he has three or for ex wives, each younger than the previous.
If the 90% have that kind of power, they could have already voted that only the ten percent pay taxes. As far as increasing the amount that 10% pays, that is a size of government question, not a how to distribute the tax burden question. As I said, no Republicans have the political will and the political clout to reduce the growth in government, much less the size of existing government.