Infield Fly

Since it came up again recently, with Sosa’s base running gaffe on the infield fly.

In theory, why isn’t an infield fly a dead ball? The batter is automatically out as soon as the ump makes the call. 99% of the time the ball is caught regardless, and when have we ever seen a runner tag up on an infield pop up. Even if the ball is dropped, most likely the runners aren’t going to advance as an easy throw will result in them getting thrown out. Just call it a dead ball, batter is out, and play is dead. Any thoughts?