How do you counter Gary's point though? What if the referee interprets something as a dive when it wasn't? For example: Gareth Bale was travelling at so much speed that a little knock on his knee knocked him over, and it was a definite penalty. But, at normal speed and at a certain angle it looked like a dive. By your logic, sending Gareth Bale off -- their most influential player -- is the correct move. Not only would he miss that important game, but he would miss the next three for something he hasn't done.
It's not the way to go. Yellow cards are fine, and maybe if the dive is completely blatant then action by the FA (fines, missed games) could be implemented, but you seriously can not do much else. Let me paint you two more scenarios.
1) If you run into the box, skill past the player but there isn't an opportunity on goal, and their player has left their leg out which does obstruct your movement forward, is going over the leg and falling to the floor a dive? You might say yes, but if that leg that should not be there is in some way effecting your movement forward which is effecting the attack illegally, isn't that a foul? Look at how fine the margins are.
2) If you are running into the box again (or anywhere else on the field) and a player behind you is pulling your shirt, is going down without force a dive? Pulling your shirt isn't enough to push you to the ground but the referee would not give you a penalty if you stay on your feet, so is falling to the floor without being forced to a dive? If such a player didn't fall to the floor, then he is being illegally stopped by this shirt pulling isn't he? That's a foul, and if he is fouled, it is a penalty.
Gary sums it up better than I can on a post, but he is completely right.