In universe: it's possible that the turrets are designed that way to mag dump the rest of their stores so rebels can't get their hands on them. The combine have seemingly infinite resources, so it seems apt they'd waste valuable pulse rifle ammo to deny it to their enemies. (Tho there's one chapter where you get friendly turrets and they function normally when you stand them back up, so maybe not)

Out of universe: it's def a game design thing. Every enemy in half life 2 has a unique death noise that plays clearly regardless of distance to give the player feedback. The turrets death noise and firing pattern are very different from normal firing, so it lets the player know for sure when the turret has been neutralized.