Part of it is everybody knows exactly what's happening, but one dude has one job, and that is to put the rudder exactly where it's supposed to be and hold it there. It isn't actually like there's something that holds the rudder in position -- it is manual, like driving a car, and the rudder will move if not held in place. Also, the order might not be rudder left 5, it might be steer course xxx. Then they use their training to hold the ship on that course.

Another thing not always obvious is the conning officer is in training to be the Officer of the Deck. He/She is learning the exact characteristics of the ship while qualifying for the next higher position.

Yes, you are absolutely correct that this can be fully automated -- and it is in merchant ships. Warships are a bit different, you want instant responses, you want people who can think and issue the right orders and people who can evaluate those orders. SN Timmy isn't stupid -- if conning officer is in the middle of an unrep (alongside another ship) and says right instead of left, SN Timmy will repeat back the order, and ten other people heard that order and there's room to stop the disaster before it happens.

You've absolutely got it where merchant shipping is concerned. Warships are different.