*Membership spots not really limited!
Then you need new history books.
History is replete with empires with much greater wealth disparity that saw no revolution, no people rising up.
It's actually laughable that you think "income disparity" drives revolution. You could make a plausible case for abject poverty, but not income disparity. Revolutions are fought on hungry stomachs, not people longingly looking at someone else's Rolls Royce.
Have you seen America's poor? As a lot, they ain't hungry.
Clearly, that's why we have all the same empires we had 1000 years ago. Oh wait, pretty much no one has the government they had even 200 years ago.