I see both sides of the issue, but there are certain situations where in keeping to the theme of "Captain" of the ship, I would much prefer that one of the other crew members handled something while I'm busy. Just the other day, I managed to stall an engine while taxiing to the active. As it was, I had to stop the airplane on the taxi way, and re start the engine myself. I must have flooded it, or it was fouled, because it took me several tries. I would have much preferred, in that case, to simply click a button on the Control Popup and direct the Engineer to dick with number 3, while I continued my taxi. Simply hitting the gamey "autostart" button would not have been appropriate in this situation. I say get rid of the AutoStart button and replace it with 4 small radio buttons that simply direct the FE to
realistically start an engine of the Captain's choosing...it would become grayed out once the engine is running. There wouldn't be any use for such buttons to shut the engine down, because as Oksar says, it is as simple as pulling off the mixture.
That said, I have Ezca and Track IR as well, and it is no big deal to jump to the FE station, but I agree with VB2 that it would be in keeping with the consistency of having the virtual flight engineer. You see, in the make-believe world of FSX, I don't feel that it is somehow cheating to have certain things performed by another 'crew member', I've already played the role of Flight Engineer on the 377, and feel comfortable doing it myself, but now I have been promoted to Captain and it is time for my henchmen to push certain buttons.

(which to a great extent the FE does, just not in this case)