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I would challenge that any society which has any significant amount of wealth disparity wouldn't eventually devolve into "whoever makes the most money gets to make the rules". Money is an abstraction of human value, so if one person has significantly more abstract-value than most people, their power and influence will always be more than people who have less even if it isn't as direct as our system via eg lobbying. On top of that, any economic system which has even the slightest asymptotic behavior towards wealth consolidation will eventually have wealth disparity.

Personally I like economic systems that use money as a price signal because of how decentralized it can be, but I'm not sure how you would avoid these tendencies without some major overhaul in the fundamental principles. Market socialism is at least better, since no one solely owns the means of production so it's harder to accumulate wealth but I wouldn't go so far as to say it isn't possible at all.

Maybe a change in ethos like you said, competition can inspire innovation but it can also lead to tremendous waste as competitors reinvent their own wheels. Encouraging cooperation in tandem with competition could produce a more well-rounded society, but there will always be sociopaths who want power for its own sake and will naturally rise to the top and ruin whatever good thing we have going on. Maybe something like radical anarchism, which rejects (unjustified) hierarchy and makes it exceptionally difficult for anyone to gain coercive power? Fat chance ever implementing something like that, though.