I agree that pet insurance is a rip off but I'd be nervous not to have it. Saving up and paying as needed sounds OK but if an animal requires complex surgery or some other complicated treatment the bill can be extortionate.
About three years ago our dog needed surgery on his leg which, including all the X-rays, consultations, medication, special dog brace, stay in hospital, after care etc., etc., etc., came to around £7,000.
Fortunately we had full insurance, which paid for it all bar the excess. We had deliberately purchased a "whole life" insurance which, although more expensive, was meant to guarantee that even if our dog was treated for the same ailment/injury one year, we could still claim in following years if the ailment/injury occurred again. However, when it came near to renewing our insurance, we were told by the pet insurance provider that the underwriter was no longer operating in this country and a new underwriter had been appointed. Although this underwriter would give "whole life" cover in the same way as before, it would not provide cover if our dog had the same problem with his leg.
We stayed with the provider because moving would have been even more expensive and previous ailments/injuries would not have been covered anyway if we required a "whole life" policy. It's worth bearing in mind, that even supposed "whole life" policies can be wriggled out of. No wonder people are cynical about insurances.