I had the utmost for the FEs during my RAAF days where on numerous occasions they got us home with serious ingenuity and resourcefulness. Although I did not fly airlines I believe FEs were not allowed to do any maintenance away from base.
I also recall that Ansett had FEs on their 767s due to union pressure.
It was also interesting that in the Ansett 747 incident at Mascot where the nose wheel failed to extend following an inflight engine shut down, a contributing factor was the FE failed to recognise the undercarriage indication. He had been a 767 FE who transitioned to the more complex 747 without being given sufficient training to step up to the more complex engineering systems and FE operations required for the 747. This was apparently due to a strict time schedule to get the first 747 schedule into, I think, Osaka and continual delays to the ground and simulator training program.