Turrets do nothing in ARAM
Why do they shoot so slowly and do so little damage? They might as well not even be there for all they do to deter enemies, especially if you're a tower diver. Feel free to kill the enemy team as many times as you want under their own turret, you'll only die to it like 1 in 10 times, if even that.
The only turrets that actually pose a threat are the ones guarding the crystal, esp if you're playing a mage, they lock in on mages and other squishies like homing beacons, the rest are a joke.