It may be a flaw as what you may have pointed out, but I'd prefer to think that this makes it a little more interesting - if the cat quiz rewards are better for you, you would skip ninetails (in other words, the top damage dealers that choose to start on ninetails would have a greater % of the fight and therefore get more coins/xp). The invisible hand of economics would lead to an equilibrium whereby the players themselves would decide at what participation level for both events would be considered "equal" in terms of rewards. For those skipping the cat quiz, they get extra xp/coins from what they are used to (see above), and for those who actually chose the cat quiz event, they probably chose it because they felt the rewards were better than what they could have otherwise gotten from fox.
In other words, I think that its interesting that players have to choose what they want to do in the game at that timing (adds a fresh aspect to the boring grind of repetitive daily events) but I guess this opinion may not be shared by the majority of players and I respect that :). Maybe they will change it eventually, who knows.