The question is how make the issuance of and access to money egalitarian on the one hand.
What about work? What about merit? What about talent? Sorry, but issuance and access to money shall never be egalitarian. No way!
Especially as some people will lose, spend or give away their fair share and end up with nothing.
They will then complain that the system isn't fair as some who saved, stole or somehow acquired coins would be rich in the new world, just as they are under the current system.