Sorry Umair, I have to respectfully disagree when you say “Let us say we give free education to everyone. Some genius creates a cure for cancer. Everyone benefits, even the rich. No one loses.” Wrong, all those currently benefiting from paid education and cancer treatment will lose big time!
The problem is not wealth inequality, this is just a consequence of the real malady, namely, a zero-sum game world. You see, it would not matter how many trillions some has, as long as the rest of the world has been guaranteed at least their basic human needs and everyone plays the life game under the same rules!