Though that is something they consider, they really just want to have more ways to interact and engage with their friend.

"Acknowledged. An incentive: the level of functionality of the shower depends on how well the game is played."

So like, if she ever wants to be comfortable bathing again... true, she doesn't have to beat Legion specifically, and there are non shower related games, but that is the one with the scoreboard, and being good enough to beat Legion would basically ensure comfort.