Elimination fights the reason people opened a party game
Most groups are not gathering to optimise a tournament. They want everyone talking, reacting and producing stories they will repeat later.
Removing the first person caught asks the least fortunate player to become an audience. That can work in a dedicated strategy session, but it is a poor default for an app passed around at a party.
Short rounds let failure become funny
A Bluff Club round usually takes three to five minutes. Being caught creates the reveal, changes the score and immediately gives the player a fresh role in the next round.
The room can experiment with risky clues and ridiculous persuasion because a mistake has a small, visible cost rather than social exile.
Scores preserve stakes
No elimination does not mean no consequence. Correct votes, successful escapes, secret objectives and final guesses all affect the scoreboard.
Party Mix carries those results through several modes, then awards titles based on what actually happened. The competition survives while every person keeps playing.
The practical house rule
If your group wants more intensity, raise the social stakes rather than removing people. Let the round winner choose the next pack, make the lowest scorer give the first clue, or award a harmless end-of-night forfeit.
Keep every player in the circle. Suspicion is more useful when it can move around.