There are two huge reasons, from my own experience, to get insurance.
Reason #1 - one of our dogs fell down the stairs and broke her neck. Result: £10k in vet bills. Sadly, she died a year later from seizures (unrelated), but we gladly paid it...we didn't have insurance at the time, nor a huge amount coming in. Took about 3 years to pay off the resulting credit card bill.
Reason #2 - another of our dogs had complications after being spayed, basically meaning she couldn't completely control her bladder when very relaxed or sleeping. The result of that is that she'd need medication for life, which completely fixed the problem with no side-effects. We'd learned our lesson, so we had insurance with whole-life cover (rather than annual), which means that the insurance company picks up the tab for her entire life. It costs them about £80/month, whereas our premium is £35/month.
So...yeah, insurance is definitely a good thing. On top of the insurance for all three of our dogs, we have a £50/month standing order to the vet which just builds up - think of it as a savings plan we can only spend there (we're never going to be without dogs). That means that, no matter what needs doing - whether it's worth troubling the insurance company or not - we never have to worry about the bill at what's usually a very stressful time.
When it gets over £800 or so, we normally tell the vet to take half of it and pay the bill for someone in need of help. We've been in desperate need before, and others have helped...so it feels like the right thing to do now that we're in a position to help others.