The problem here isn't that people don't want to win the Cup. The problem is it might not be financially smart to do well on the Cup.
I would love to win it, and I would even lose some money to do so, but I won't lose THAT much money to win it.
Yes, 'cause right now I would lose money to do well in the Cup. If I won it I would grab an extra 650k, but I would have to suck in the league and lose fans for the next season. Plus, given the 40% cut, I have now a margin of less than 30k weekly profit if I get full arena every game. Not doing well on the league is not an option for me, it's a necessity. Losing the Cup, therefore, is a necessity for me (well, not losing, but not fielding my best players in it, which will ultimately lead into a loss anyway).
It wouldn't at all be a good idea to trade my arena income for cup money. I would go bankrupt for sure.