Just a quick update.
There have been a few threads re the appropriateness of credit card based travel insurance.
On this trip I originally sought advice on, it turned out that I did need to rely on the insurance for the loss of a piece of hand luggage that was left in a taxi on the way to the airport. With a toddler in tow, a full boot and a couple of items in the front & back seat of the taxi, one of those bags got left behind which happened to contain mostly new high-end store purchases that I didn't trust to check in and was to be hand luggage. Even the luggage itself was new!!! Luckily it was only one bag and a smaller one at that, having departed for HKG with 2 suitcases and coming back with 5, I would have hated to work out what was missing in one of the larger cases.
Axa were very helpful, everything got sorted out relatively quickly compared to previous experience with "specialist" travel insurance companies, resolved to my satisfaction, they rang when they said they would and things got done within the timeframe promised, a very pain free experience.
Obviously situations vary and perhaps if it was a different type of claim I may have had a different experience, but now I not only feel that the Amex policy suits my needs for most trips I will undertake, but I have some reassurance in the way I was dealt with by Axa.
Also worth a compliment is the first class lounge in HKG for Virgin Atlantic. The manager dealt with the taxi company, promised to let me know the outcome by the time I landed in SYD or if not then via email, and followed it through with a couple of emails without prompting. Axa were then happy to rely on this as "reported" rather than requiring a formal police report to also be lodged which saved a bit of hassle as well.