That is not correct. You cannot play against a team from different league of the same division. To win a division you have to beat only few teams succesfully and you have whole season run to do it. Cup is about relegation battle.
At this condition is cup in fact pointless, because doesnt offer any chance to win even for a 2nd division teams (if any won the cup, Im sure that 3rd division team didnt). The problem is that you have here only frame of teams in the first two leagues. Majority is much lower and from that point of view it is not interresting, because you will always know, that you will relegate sooner or later no matter what you do.
Im not sure about basketball, but in football there are cups divided among different levels, so 1st league team will not usually go play agaisnt bunch of villagers to the arena where buy tickets mostly families of the players.
I dont know how about you, but I dont see any motivation in a long run in the cup, because you have to have extra players for it which doesnt have to cross over 50k wage, because it doesnt make big difference anyway if you are losing money because of it.