I have no experience of running an airline ... I really should make that clear.
However, I have had some 40 years in both 'operations' and 'management'. I am not an idiot.
There are still some basic principles that will always apply ... and at the top of the Aviation list are obviously 'Safety' and 'Profitability'. If you do not have the Staff enthusiastically supporting both of those principles, you have a BIG problem.
How do you encourage people to go the extra mile? IMO, by meeting them somewhere in the middle from time to time. That anecdote about Sir Richard sums up my style [yeah, I'm wonderful!] ... if Management keep Staff at arms length, instead of engaging with them, you are doomed! I never lost any Management credibility by putting the kettle on in the crew-room ... it was just that at that moment, everyone else was busier than I was. No big deal, I even do that for my wife occasionally
"Arrogance" breeds opposition. A bit of humility goes a LONG way.