The chief engineer is still the best at fixing. Other crew might be able to nail a plank in to fix a hole - but not much more than that. Even if it's coordinating a bunch of "able seamen" or "able crewers" - the Chief engineer should, generally speaking, never be on the quarterdeck in this kind of crisis - because their skillset is so valuable, and so needed at work.
Some crew are much less useful - and they can be spared to run errands, carry messages, etc. The Chief Engineer cannot.
Think of it as like Star Trek - except, there are no communicators - so the least necessary crewmembers, have to act as living communicators.
If Scotty or Geordi La Forge is out of Main Engineering and on the Bridge - during a space battle, something has gone very wrong with his priorities.