Most airlines only type captains in equipment becuause type rating = money. When my husband went to 767 school with TWA they typed him in the 757/767 (common type) because all 75/76 crews did international, and they needed type ratings for the long-haul routes. I think he said it was about $10,000 worth of type ratings TWA paid for. It would very expensive to type every pilot.
FEs are trained as Flight Engineers on whatever aircraft they're going to be an FE on, not as first officers or captains, or given a type rating. Again, any additional training = more money to spend. Nobody hires PFEs anymore, so if someone is a flight engineer, s/he's a pilot, and if the sh#t hit the fan, I have no doubt the FE could land the plane. Engineer school is tough, a flight engineer has to know the aircraft's systems very in depth. I remember Bill studying in TWA and Delta new-hire schools when he was checking out on the 727 panel, and thinking "damn! this is a LOT to learn!".
Sorry to ramble, hope I shed a bit of light on things......I'm sure Doug will have more specifics to add!