Why are you assuming that “fairness” requires a linear distribution between ability and wealth? A winner-take-all system may be undesirable in many respects, but it’s not necessarily unfair.
My point is that having tycoons with 1,000,000 times the wealth of the median person is not a fair distribution, no matter which reasonable function you choose.
If you think superficially of "fair" like in a game, then yes a winner-take-all system can be fair. But when talking about socioeconomics, I think fairness goes a bit deeper. For example I would say a society with a lottery that picks one winner and tortures all others is not fair to those who lose (even though it's game-fair).