equal power does not mean "everyone is exactly the same". It means everyone has equal say in how things work. No one owns anyone else. No one has dominion over anyone else. Think democracy.
No one has dominion over any one else... lol good luck. That sounds a lot like equality of outcome to me.
"Democracy is two wolves and a lamb voting on what to have for lunch. Liberty is a well-armed lamb contesting the vote"
A pure Democracy is where individual rights are sacrificed at the altar of mob rule.