I was watching TNG the other day for the first time in years and I had to ask myself if there is any need to helm or navigation. Surely the captain/first officer could just tell the computer where they want to go and when they want to arrive by, and the ship can steer itself.
Captain: "Computer, Set course two-one-three Mark seven."
Computer: ""Unable to comply, the automatic pilot system is offline."
Automation is all very well and good, but like any system it can fail. Today a plane could take off, fly to it's destination and land all by itself." But would you fly on it without a pilot?
As for having a dedicated department, sure everyone might receive basic training in piloting a starship, but their is a difference between basic and advanced training.
The problem is that actual human technology of 2013 has surpassed Starfleet technology of 1966.
Completely automated cars and aircraft are right around the corner and if I was on the newest technology fighter or airliner today I think I would rather have an incapacitated pilot then an inoperable computer.
With the new systems man just can not keep the flying things stable on their own even if he is Chuck Yeager or Hikaru Sulu. The trick isn't running evasive action sequence gamma or changing course to 124 mark 12.5 the trick is just staying stable and not tearing itself apart in the process of flight.