You still thinking to much in terms of trying to eliminate the wealth gap. It will always be there and it will always sound bad, but again it has never been this bad. It's only this bad because of policies. If those policies are reversed and some programs are implemented to build wealth for lower classes, you could close that gap. The rich will still be rich, but the poor will be less poor.
I think one think you're not acknowledging is that money at any level means more to the poor than it does to the rich. If you shrink the gap 10% for example. That doesn't really mean that much at all to the rich and it doesn't sound like a lot, however on the other side that might mean you brought a lot of people above the poverty line which is good.