I've had these experiences:

Getting stuck in traffic in Vancouver and was going to miss my flight home to YEG. Called the concierge and she printed my bp, met me at security, and rushed me through and onto the flight at the last minute. There was no way I would have made the flight without that!

Oversleeping....happens to all of us once in a while, and when it does, calling the concierge is very helpful. They know that when you say "I need to be there by x:00," you mean it! They will think of the strangest routes and search high and low to get you where you need to go! I once got from YEG to YYJ via YLW and YVR....I got there by noon, and I didn't have to buy the nearly $900 one way Y fare via YVR alone!

Living in YEG, snow is a reality, especially with the Dash 8's that fly to YYC. I have had the concierge call at 5am to tell me my flight has been cancelled because of snow, and whether I'd like to go on an earlier or later flight instead. Sometimes they would call before the flight showed up as delayed/cancelled on the FIDS!

In irregular ops, they're amazing. I was once diverted to calgary because of a cracked windshield enroute YEG-YYZ. There were 2 agents in YYC to meet the full A320 and rebook us all....Called the concierge in YEG to check what the last flight of the day to LGA (my final destination) was, and the loads. She checked and said it was at 20.30, and it was half full. She also said that because AC changed the flight number on the new flight to YYZ, she couldn't rebook me, and I'd have to let the YYC agents do it. Just having her check that was great, as it let me relax all the way to YYZ, and not worry whether or not I'd get to NYC that day!

As SE, I never used the concierge much, I always looked at them as more of an "emergency" or last resort assistance, for which they are great!