And whence the money for the share? Taxes. So this is just a UBI.
This, like all UBI proposals, seems like a way to dress up a massive tax hike: "but you'll be getting your share of GDP!". The only way to get me to like a UBI is to have UBI replace absolutely all (and I do mean all) welfare programs so that we can just haggle at every election over one headline UBI number + necessary taxes. And the initial UBI and tax rates would have to be no more burdensome than the current total of welfare it would replace, and preferably significantly less burdensome than that. Many UBI proponents, of course, would not mind this because they'll aim to ratchet up the UBI and taxes for it in a way that becomes culturally irreversible -- and that's a reason to be against UBI.
And incidentally, all instances of "soak the rich" in American history have actually been "soak those who aren't rich but have high incomes". The truly wealthy have no income as such -- instead they have capital. And why don't we just tax capital? Well, because every time it's been tried anywhere it's been a disaster for the overall economy: capital (and wealthy people) flees.
I'm ready for the downvotes, by the way.