Regulatory capture and anti-competitive regulations seem like they would have a much bigger impact on wealth disparity than tax rates.
That's how this bogus article starts, it says "the poor are not better because so much is owned by the rich", a "Look, a squirrel!" head fake which totally ignores how well off the poor are or aren't. And you're just continuing that focus.
Bottom line: do you care about the poor, or about the rich?
Your statement above only touches on the latter.