People have been trying to fairly distribute resources to give everyone a basic standard living for ages. It's the basic idea behind welfare, socialism, and communism, there's a precedent for trying to do exactly what I described as the CPAI.
Why would people follow it? Why would some rich and powerful guy with connections forgo all his power to some CPAI that was set up? How would he maintain his ego when the world no longer shakes from his every footstep? How would he repay all the favors he made to those that got him there?
AI is just a tool, like the gun, the ship or the railroad. It's not some panacea that is going to protect human nature from itself.