Not sure where you got your numbers, but they are wrong.
Actually, the top 1% pay about 40% of the total revenue collected by the federal government. There are 3.6 million taxpayers in that group, and the vast majority pay at rates between 33% and 39.6%.
There are a number of people in the top 0.1% that earn the vast majority of their income through investments. Those people pay 15% on every dollar they earn that way, above any standard or other deductions.
There are some extremely wealthy elites that fit your description, such as Warren Buffet or Bill Gates. They have the kind of power and wealth (and tax attorneys and lobbyists) that they can shift their tax burden into foundations, foreign countries, and other avoidance schemes to end up with very low or non-existent tax liability. They really don’t need income at all, and if they don’t have income, there is no tax.
But at that point you’re talking about the top 0.0001% at most.
If you want to capture more taxes from those ultra-rich folks, vilifying the 1% and raising rates will not work. In fact, attempting that could end up with lower revenues. It would require a wealth tax instead.