So the SO could potentially have greater situational awareness?
One of the problems for any pilot, especially in complex aircraft, is basically tunnel vision. When things go wrong, it's very easy for that problem to be like an attention black hole...pulling everyone into watching it, rather than keeping an eye on what the aircraft (and others) are doing. So, we train to manage problems with someone always designated to flying the aircraft, and whilst any issues are looked at by others. That's part of the meaning of 'flying pilot' and 'non flying pilot'. SOs can be in a position to watch both sides of the equation, as they aren't directly involved in either.
Do you have an example of SO assistance that was worthwhile?
QF30. The SO was off watch, but immediately came back to the centre coughpit seat. He didn't say anything, or ask what was going on, but worked that out for himself. His first comment was useful though...."the off track safety height is 8,700 feet".
After a dirty go around due to unsafe landing gear in LA, the FO was having trouble getting the FMC to accept the landing data. SO reminded him that it needed a cruise altitude to be entered (which is a minor quirk of the FMC).
A really nasty morning in London. Most of the alternates were not available, and lots of planning had happened during the cruise establishing 'what ifs'. The final plan was to fly one approach, and if that didn't work, to divert to Stansted. Whilst the weather was the same at Heathrow and Stansted, the runway alignment at the latter meant that wind was within the crosswind limit. SO took it upon himself to listen to Stansted tower during our approach to Heathrow, so that when the go around did happen, he was immediately able to point out that Stansted had also gone out of limits. So, jump straight to option two, and go to Amsterdam.
They are part of the crew but with a different view. Their input is used day in and out.
If SO communicates with ATC, does Captain and FO also listen in?
With occasional exceptions, ATC comms only happen from the front seats. So, if the SO is taking to ATC, then he's one of the pilots on watch. Everybody listens to ATC. The exceptions....well, departing Dubai, you had to call an Iranian military frequency before reaching their airspace. They only wanted a few details of the flight, and did not issue ATC clearances, but the call was required during a period that was pretty busy. If you had an SO, they'd take care of that.