the other players have no incentive not to sabotage.
In real life versions of The Mole, the non-mole players work together because they want to earn money to win. But when there's no money involved, the only objective for the players is the win itself--and it's more likely for them to win if the players they're competing against think they're the mole when they aren't.
(Pretty sure this has been noted in this thread before, but it seems to have been forgotten in the last several posts.)
The advantage of the "two concurrent games" idea is that it provides this incentive for the players not to sabotage without involving real money.