I think the relationship isn't linear. Too much equality and there is no reason to go above and beyond, to innovate or to take risks. To much inequality, and we find the same result. Enough inequality to reward those who do more (with some understanding that there is elements of luck), but not so much inequality that people have to be lucky to succeed, if it is possible at all.
You want a game in which early levels are easy enough that it won't take too much skill to get through. [Basics of society, access to housing, clean water, health care..]
As you get to higher levels, there will be challenges that some players can't get through [amassing enough money to buy a yacht], but that's OK.
Some players have cheat codes not available to other players [laws to help special interests] because they have an in with the game designers [government], and that's OK too as long as it doesn't go too far.
It's not a big deal if the most skilled players can get to really high levels - that's not the issue.
It's when the most skilled players make the game unplayable by the average player that you have a problem.
I think your example is too simplistic. There are more dimensions to equality than just wealth or money. People could be socially rewarded but still be on very similar wealth levels. There are some people actually persuing this as a life goal, it‘s called earning to give and comes from the effective altruism movement. They try to get into a really well paying position but give most of the earnings (like 50%+) to effective charities. It‘s not always about money for yourself but being able to work for something you believe in and a recognition of your efforts. How else would you explain suicide bombers and soldiers giving their life in unprofitable ways?
