Yes, I agree that you are right. If you have to lose, the game is likely to lose its fun. I would probably prefer not to include it.
It's always good to have plenty of adventure potential in a game, in a way that requires the player to go unconvential ways and perhaps not even advance in the game or play purposeful; a sandbox effect within the game, so to say.
Maybe you'll find a middle way or an alternative for it.
(Also a gimmick to increase replayability btw, hehe)