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Ours has insurance for similar reasons. Sad to report the insurance companies have very carefully worded policies to tip things to their advantage. Some of us will win though, it's kind of a mutual fund run for profit where all of us who love dogs chip in and help each other through tough times (really optimistic world view there).
I guess we all pay and hope we never need it too. When ours had an emergency operation we were very happy to have the insurance. Now I try to forget how much the monthly payments keep going up.
It's also near impossible to get registered with a non corporate conglomerate vet in SW London.
A friend was working on legal stuff for pet insurance and told me categorically it's not good value.