Crap, this could have really saved me over the last month - what's the catch? Have you used something like this? I think my last card had it (calling it "Concierge") but my current bank doesn't mention it anywhere.

Typically cards with extra features either (at the low end) charge a monthly fee or (at the higher end) have minimum requirements such as a minimum net worth for the holder or a minimum monthly or annual spend through it. Lower end would normally be a small fee and fairly basic bonus features (travel insurance, gadget insurance, airport lounges) while I'd expect any half-decent concierge service to be aimed at attracting richer customers. The minimum worth/spend requirements basically mean the extra services offered are there to attract people who will give the card creators more % by spending more money, giving them enough profit to offer free services.