[1rudeboy]

I've spent a little time pondering it myself. The best I can come up with is that stopping the clock is worse than running it. If you stopped the clock, the players would have no incentive to (quickly) return to play. You would ruin the continuity of the game.

The system now is probably the best it'll ever be (referee keeps time; injury time announced at end of half).

[GOP_Raider]

That makes sense now that I think about it, since I considered it to be a six of one/half a dozen of the other kind of thing--i.e.: why tack on extra time to the game when you could just stop the clock?