Hi!
I'm personally a vet myself but also have a cat that is fully insured, so hopefully I can give you some input.
In my experience, I can see many benefits on insuring your new pet. Here in the UK veterinary treatment is getting more and more expensive each year. The problem is that sometimes, even something like vomiting or diarrhoea in a young cat, may lead your vet to perform blood tests, radiographies, which together with few medications, might easily reach already half a thousand pounds. If you have savings aside for your pet, that would probably help because in the majority of the places you need to pay up front. However, if you don't, most of the practices don't do payment plans. Some insurance companies may pay your vet directly especially in emergency situations, which I think is probably the best benefit of getting your pet insured. Also, as they get older, cats can suffer from kidney or thyroid conditions, as well as diabetes or dental disease (very expensive!!! and not all the insurance policies cover this), which can be pricey diseases to treat (as they involve on-going costs). It might not be something that you need to worry about straight away, however the typical recommendation is to stick to the same insurance company since the beginning, to avoid conditions to be excluded between different companies.
You might never need to use your insurance company (which is a good thing) and therefore you might think that you are wasting your money if that's the case. However for me, as a pet owner, I find essential to be able to pay whatever is necessary, as soon as it is necessary (in an emergency situation), which sometimes is not possible if I don't have enough funds. It gives me that extra peace of mind. Also some insurance companies offer videocall consultations included as part of your policy, so sometimes you might not even need to take your pet to the vet if has an easy solution.
I hope this helps :)
Carla