At our veterinary hospital, we do recommend pet insurance. But we add the caveat that Pet Insurance may not be for everyone. From a long term, macro view, pet insurance will not save you money. But it may save your pet's life.
I have a web page that explains my position on pet insurance, and it also lists the 10 insurance companies that do business in Florida. Most of these do business in almost every state. If you are interested, you should research them to find one that fits your needs:
http://ormondcatclinic.com/pet-insurancecare-credit.pml
Note that we are a cat-only practice, but it all applies to dogs too. I created that page several years ago, and have fixed the occasional broken link when the insurance companies make changes. So if you do find a broken link, please let me know.
Dr. Henning's advice reminds me of the old "Sure, that will just buff out" joke we use after a major crash. But there are many people that try that. If they are ever successful, then we wouldn't see the results. But what we DO see are the cats that get brought in after such home surgery because the owner couldn't stand the stench of the gangrene. We usually wind up amputating a leg or a tail or we have to euthanize. But if it is a neck wound or a chest or abdomen wound, there isn't much we can amputate and we go straight to euthanasia. Add in cremation and an optional urn and that isn't cheap either.
Often the wife brings the pet in after home surgery, because the husband is at the emergency room having a nasty bite fixed after trying to stitch up their sweet little "wouldn't hurt a fly" Daisy after Daisy bit the **** out of him for operating without anesthesia. Such surgery can result in even more pain and excruciating death than the original wound. But of course, I have a vested interest in this, so take my opinion for what it's worth. But also take Henning's advice for what it is worth too. If you hate animals, or consider them fungible, then just shoot them instead. It is more humane. (note, that is not a recommendation).
In 15 years of practice, we have only had two invoices exceed $3,000. It would have been three, but one of them went out to the car to get their check book and never returned. All contact info was false.
We could have had many more invoices that size or more, but most people, even the ones that can afford it, choose to euthanize rather than spend that amount of money on a procedure that has no guarantee of success. So much for the theory that people will spend any amount on their pet. Like many other theories, that one doesn't survive the real live situation.
So, if you really love your pet, and you might not want to have to decide whether you want to gamble several thousand bucks "trying" to save your pet, then pet insurance may be a good deal for you. Check out my web page to help you do the research. If you want my opinion on which one I recommend, PM me.