There are three main reasons for people to have pet insurance. The first would be for older dogs because even the best dog is going to develop some health problems as they age. So you want to minimize the cost as your veterinarian and medical bills by having insurance that takes care of it.
The second would be specifically for certain breeds that are known for being very problematic genetically. There are many dogs that have known diseases because of how interbred some of there ancestors were before we knew about genetics. Then there are also horses that are being breed to be so fast that their ankles and legs break because they are so thin to support their weight at that speed. Some cats develop breathing problems as they age because of how flat faced they are. So there are some realities that must me faced if you want to buy or adopt a certain breeds.
The third is probably more practical but for work animals. My grandfather had insurance for his dogs because they were work animals. He had cattle that sometimes needed herding and if they get aggressive or scared can accidentally step on your dog. There are also instances where wild animals like cougars and coyotes can attack your dog while protecting you or your animals and you want to ensure they get the best medical help when the time comes. Then you can also consider other work dogs like the ones that work with police officers, firefighters, and military. These dogs are trained to go into dangerous situations for our sakes and need this kind of protection.
So I think there is a good reason to have insurance if your pet falls into one of these categories. I typically don't have insurance for my pets until they get older because they don't need it and it's cheaper to just pay for the vet's bill instead of a monthly insurance. My pets usually fall into the first category but I don't think it's weird for people who can afford it to have it for their pets. It's only gets weird when the owners don't even have insurance for their kids but have it for the dog that I find it strange.
