No, because the _actual reality_ is that reducing inequality makes the rich, slightly less so, and the poor significantly safer and healthier.
If you tell people you want to reduce inequality we tend to correctly assume the intent is to make the poor better off, we're not AI searching for the most absolutely effective solution to reduce inequality to 0 by killing everyone or something.
I think there is something to be said for the danger of losing or stagnating the progress of the poor and middle class if the wealthy become so rich and powerful that we effectively revert to a fuedal system.
The worsening social mobility measurements are one reason to be concerned.