pet insurance worth?

hi all,

First time pup owner and I know it’s always best to set them up on a plan right away. I am grateful to be in a position that if I ran into an emergency that would result in an a costly bill I could take care of it, not that I would hope for that, and I’d still be pretty stressed out, but that’s what my credit cards for lol. However, given my situation, is there really any savings apart of an insurance plan? Regardless, in the event of an emergency you’d have to fork up the money anyways, and wait to get reimbursed. Does it make more sense for me to have my own savings account? I did some basic math and $100 a month premium is $1200 a year, now if something happened that cost $3500, with a plan and 90% reimbursement, it’s essentially $350 so Id be saving (not including deductible), and would equate to about 3 years of monthly premiums. I know it can provide peace of mind to many people, so just trying to gauge what everyone’s thinking. I’ve had pets my whole life and have never considered it. My old boy is 13, and in the past 9 years I’ve had him I’d say I’ve spent about $7000 including some surgeries, shots, vaccinations and misc items. That’s about $800 a year, or $65 monthly. Most of the bigger expenses came with his age, later in life. I know I can’t predict the same but it’s a general idea.

All opinions appreciated !!

Edit: typo