A lot of the gameplay in TTT is deciphering who the Traitors are, protecting your detective, then killing those traitors. I think what makes TTT the most fun are those moment where you feel that the round literally depends on you. Winning those situations where you feel outnumbered is really satisfactory, but lets say it wasn't, and that didn't matter at all. By making it easier in this way, you're effectively deleting the basis upon which you were playing the game for the whole round, as you do not have to piece together any clues or have any sort of meaningful suspense, as whether or not you are suspicous of someone no longer matters, and there are effectively no traitors. Just a 1v4.
By giving Innocent's an edge in this situation, you're taking away all of the Traitor's work over the course of the round. They worked as a heavily outnumbered force to kill off everyone without getting caught, they played well, but now they're at a random disadvantage. Just feels weird, that's my 2 cents.