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I put myself badly, lets give it another bash.
You see, the way I see it, if there is that large gap you have a situation where the tax rate can afford to go up on the top end.
These taxes don't go up just for the sake of the poor though, they go up because you have expenses and they need to be paid.
The wealth gap would not be an issue if America was in a surplus position, but when that wealth gap is present and you are in a huge deficit position, you need to consider the super-wealthy as your first source of income.
The gap would not be so wide, if the wealthy really needed that extra money.
Now of course some of this additional money goes into wealth redistribution, it has to. The guys you hire to fix your roads, will be poorer than your average CEO - but the trick is not to simply give money away, but rather find ways to make that money work for the country.
What your argument seemed to me to be about (I could have misread what you meant) was the idea that the income gap is meaningless. It isn't, it points to the most painful truth of how to get out of trouble, the truth that FDR figured out and got called a "Class traitor" for, that the rich can afford to pay higher taxes.
The trouble is, the rich are also the guys who own your media and your government. This means that this source of potential money gets ignored, and the general idea of higher taxes is sold as being about giving the money away to the poor.
This is also why in the past, income disparity often predicted social collapse - the rich were comparatively sheltered tax-wise, which meant higher taxes on the poor, which meant revolution as the poor got sick of starving.