I think the problem with the straight red for any offence is that it makes the referees much less likely to call it. You already see that with lack of sending off for 'last man' fouls.
You might be right on the extra deterrent though, I'm not sure what would happen there.
I would like to see far more yellows given for sure, but it is very difficult to pick up on in real time, and refs are reluctant to accuse people of cheating, for obvious reasons.
I know the other team doesn't benefit immediately from retrospective punishment , but in the long run everyone will benefit from cleaning up the game.
Will also have a "name and shame" aspect that might be a deterrent.