Well, here (Austria), vets aren't that expensive and I have enough money on the bank so that doesn't really make a dent, although I'm there way more often than I'm at my doctor

. Vet visits rarely go over 100€, a skin tumor surgery on a dog was 250, a rabbit spay 130, neutering a buck 90, the most expensive was trying to save a doe with blockage through surgery in a vet clinic on a weekend, unsuccessfully, that came to 350, that's ok for once in 15 years.
Generally speaking, my issue with insurances is that others have way less qualms to use it, even using all kind of tricks to make the insurance pay - I don't, can't do that. I would need to be really desperate to accept anything, so I definitly pull the short straw there. Also, the companies do it for profit, we all pay more than the actual - summed up - cost is. For risks I can cover that all makes it not worth it for me, putting the money aside others pay for all kind of insurances is an insurance in itself. After decades of being reasonably lucky I'm pretty safe.
I do not have any insurances apart from the mandatory ones, like, for the car. I considered keeping the insurance for the house when I bought it- just basic fire, storm, water, but the company said no, I need to take a package with 50 other things I do not need, making it absurdly expensive, so I quit that too.
Anyway, my point of view definitly is different since bills aren't in the thousands here, and since I have enough wiggle room to cope with whatever is coming my way. I reckon that under different circumstances insurances make sense, but imho it isn't something to cope with costs that are to be expected - in that case imo you're better off putting that money aside from the start.