Wouldn't it be already enough to have the pools split, but each of them get the same share?

Bronze: 20%
Silver: 20%
Gold: 20%
Diamond: 20%
Champion: 20%

I would assume that the amount of players gets less and less the higher they are ranked. So naturally one would be incentivised to climb to a higher league. This way people in lower leagues would still earn less than in higher leagues, which would prevent mass botting and encourages card leveling to climb further