Yeah, I generally don't have insurance. The first time I had an insurance policy was when I visited Europe last year (I've moved here now). I had top-reviewed policy. In the last week of my trip, a complication with busses led to me losing all my luggage. It took over 6 months and a lot of stress and hassling to get any sort of pay out, because the bus company had simply claimed "not our fault" and the burden of proof lay with me. After this + witnessing insurance companies ruin lives in the wake of natural disasters (the Christchurch earthquakes being a personal example), I have suspected, long term, the average insurance purchaser might be best suited to paying their monthly policy cost into a savings account.
That said, that was the first time I'd had insurance, and I did get paid out a lot more than I paid for my policy (and more than I'd expected, actually). Whether it was worth the stress and long term headache, it's hard to say (probably not).
I'd be interested in your hypothetical as well. I don't know how it works. I do know a number of hikers and climbers who've settled outrageous bills for injuries and rescues when out and about in other countries. What would've happened if they didn't have insurance - I have no idea.
In this case, if my kit were to be lost again, I'd be very upset (especially given recent history), and as someone with... nearly no financial assets... the complications a rescue bill or foreign hospital could ruin me to the point of having to ask family to buy me a flight back to NZ etc. I don't how know they would enforce whatever I would owe?
The AAC kind of makes sense in terms of getting other benefits - such as huts, if you just want accident cover.
Nationwide is cheap (£13 a month, and I can just switch my account back to a cheaper option when I am no longer overseas) and has other benefits - cheaper overseas withdrawls, etc. So either of those options do sweeten the "peace of mind" scam.