I won't mention any company names but I've had positive and negative experiences with dog insurance.
First experience ever was with my first adult dog I got in 2008, first of all the company wouldn't pay anything to do with my dogs heart murmur because it was from birth, which the vet said was pretty unfair, and I used to change companies to get the good price and most companies reel you in with a discount price then hike up the price after a year which happened to me every year, so after one year my dog had a fit and so i changed again at the renewal, then when he was diagnosed with the cavalier brain disease the insurance company didn't pay out for the MRI scan, the hospital which did the MRI scan helped me appeal, we did it 3 times but still they wouldn't pay out. So I learnt my lesson. After that I cancelled my insurance and paid money in a bank account instead which worked when he needed pills every day. The vet said that way is a good idea if you have a big lump sum. She also said would you be able to afford if your dog got run over and pay out of your own money, if not then you need insurance.
So when I got my second dog I chose the same company and now I can't move because he has been diagnosed a heart murmur last year.
For my goldendoodle it's been more straightforward, most insurance companies have a 2 week grace period for illness and 5 days for accidents. I have been changing every year so far over the 3 years because she is healthy and no underlying problems. But I am hoping to stick with the same company I have just got insurance with.