Most dogs that bite are not strays. They belong to a neighbor, a friend, a family member, someone at a barbecue.
Families come to a decision point that no one prepares them for, usually while a child is still in bandages: pursuing this feels like an attack on a person they care about who is already devastated.
Here is what is worth understanding before making that decision.
The claim is against an insurance policy. Practically speaking, you're asking an insurance company to pay for an injury it collected premiums to cover. Your neighbor's role is to notify their insurer, which their policy requires them to do anyway.
The owner is generally not personally out of pocket where coverage exists and the claim falls within policy limits.
A claim is not a criminal matter and does not by itself determine what happens to the dog. Animal control decisions follow their own process, driven by the bite report and local law, and they happen whether or not anyone makes an insurance claim.
Being honest about the other side of it: it can be uncomfortable, and it sometimes strains a relationship. Insurers occasionally take positions that create friction between people who were on good terms. That is real and we do not pretend otherwise.
What we would say is that a family with a permanently scarred child is weighing that discomfort against a lifetime of medical decisions and costs that someone will have to pay for. Those are not equivalent things, and the choice deserves more thought than it usually gets in the first difficult week.