The more you repeat that you find flipping that switch repugnant, the more you prove the point that inequality itself is not the problem.
Inequality is the problem
Let's run with that.
(1) Inequality itself is the problem: "the problem of inequality", "The vast gap separating the top and bottom"
Flipping that switch reduces inequality.
By (1), you should flip that switch.
But you've stated that you don't want to flip that switch even though it reduces inequality.
Hence inequality itself is not the problem.
Tyler Cowen, professor of economics at George Mason University said it best:
"
The broader philosophical question is why we should worry about inequality — of any kind — much at all. Life is not a race against fellow human beings, and we should discourage people from treating it as such. Many of the rich have made the mistake of viewing their lives as a game of relative status...
What matters most is how well people are doing in absolute terms. We should continue to improve opportunities for lower-income people, but inequality as a major and chronic American problem has been overstated."