Even though I'm against these appeals, I can see your point, Levi, however I'm afraid this would raise another problem.
You say that if the appellant is found to be wrong then he should be sent off. Imagine the following scenario - last minute corner, lots of players holding each other's shirt, ball goes close to some of these and the attacking player falls to the ground, he appeals, as his shirt has been pulled, however, the referee finally decides ( after watching the replay ), that even though there's been contact it hasn't been sufficient enough to reward a penalty. Basically it's a matter of opinion, some referees would give the penalty, others would decide against it. Should then the player be sent off only because this specific referee's opinion is that the severity of the shirt pulling is not sufficient enough for a penalty?
Don't think so. Also, if the severity of the punishment for false appeals is lowered, say a yellow card, then it'd make a mockery of the game, as every player would appeal for every little challenge that some referee might decide to be enough for a penalty to be given. It'd also be used for tactical perposes in the same way that players make tactical fouls to stop dangerous counter attacks.