It doesn't matter if you redistribute the wealth away from the non-doms - unless you redistribute it away such that they are on the median income you are increasing inequality. And as this would mean that they didn't come in the first place, nobody is proposing doing this.

And, as I said earlier, the immigrants do reach median (or higher) levels - but it takes a generation or so. And so people from a couple of generations back are now "normal", so the latest lot take their place (and get complained about by the previous immigrants, so far as I can tell).