It don't work that way. You can't just turn off animation. If one person turns it off, it'll create sync issues within multiplayer games. I believe that's a valid reason. Plus. It serves no purpose other than esthetic. I'd rather have performance
So turning off planet elevators in the options menu creates sync issues with multiplayer games?
No it doesn't of course. Since both, the moving turrets and the space elevators are graphic fluff with no consequence on gameplay, it wouldn't be a problem for multiplayer at all.

Edit: To elaborate a bit more.
I dunno about the inner working of the sins engine, but I imagine that it works something like this:
Each ships weapons check if an enemy is inside its range. If the enemy is it checks if it inside its firing arc (since Sins only has 4 firing arc possibilities (front, back, left and right) with full 180° this check is quite simple). If the enemy is in, the weapons shoot and damage is applied. Now the weapon waits the WeaponCoolDown time and shoots again at the same target if the target is still in range and not already destroyed.
Now to add turret moving, it would just need another action before/after damage is applied, the turret would move to align in the direction the weapon has shot. It continues to track the enemy until the enemy is out of weapon range or angle (which would be the same check the weapon already does to see if it can hit an enemy).
Of course, with this system the turret tracking would lag a bit behind the first shot of the weapon. But it's a very easy and also fast system (it doesn't need that much more calculations).
Now this sort of action doesn't need to be send to other clients. It can be easily calculated clientside and is of no interest to other clients. I imagine damage and when shot will be shared info between clients, but why would you want to share turret tracking info?
Now, someone tells me why this isn't possible?