I've personally lost my platinum card about 7 times and it is the most pain-free experience. Also I've had a number of fraudulent charges and amex just wipes them away. It's wonderful.
I've found Amex's concierge to be okay and their travel product prices to be absurdly high. The only reason I keep my Platinum card is because I get $200 in Southwest gift cards each year with their airline reimbursement, and they reimburse me occasionally for my Global Entry membership renewal.