But those figures are surely based on what the IRS actually registers as their personal income. The point of tax avoidance is to avoid having it registered as your own net income in the first place. By having it accumulate in offshore trusts or companies, deducting investments that are in fact for your own personal benefit.
The reality is, I would suggest, that the richest 1% are not paying 25.9 cents of every dollar that accrues to them every year, because the IRS is not aware of that money, or cannot record it as their personal income, even though it in truth is. It is instead being taxed at near 0% as the dividend income of a Panamanian holding company, or some other such ruse.
One area where I would agree with you slightly is that taxation could be massively increased, but on luxury goods.
Lamborghini or Louis Vuitton products are not required by the general populace, and would be as attractive (or more) to their market if the price were quintupled.
However, any such change would require both complex definition and above all international agreement, or else every square centimetre of Andorra would be paved over for supercar dealership lots.
Though as they are running out of snow, maybe that would be a helpful shift in economic priorities.