I had insurance with my previous dog and I am so glad I did. In 8 years, they paid out over £7000 on him. When he died at 12 years old, his premiums were still under £20, maybe because he was a cross breed. Our puppy is insured but our 11 year old staffie isn't. My husband didn't insure him after he moved in with me and trying to find a decent price for him now isn't easy. We will pay whatever vet fees are needed for him as opposed to insuring him at this late stage.
In a way, the license is a good idea, but I agree with everyone else on how it would be policed. The other thing to do is to try and get rid of the bad breeders, how this can be achieved, I have no idea and whatever method was used, you would still get some that would breed illegally.

Having 3rd party insurance is a good idea but you don't need to have a licence for that do you? I totally agree with you regarding the gun licence law but as you say it is to ensure that the people who own guns are fit to do so. How would you apply that to a dog licence? Are pro-licence people saying then that the licence would be a way of assessing if people were fit to own dogs? How would they do that? What criteria would be used?
I can only imagine that this would encourage more unscrupulous puppy farms who would be willing to sell 'under the counter' so to speak. Good breeders already screen potential buyers.
Sorry still not convinced
My point exactly. If you have strict rules that mean somthing then a proportion of people will choose to ignore them and hence create a black market, this will take a significant level of resources to counter. If they cannot do it on something that really 'matters' to society like guns or drugs, there is no possibility of their being able to do it for something as relitively unimportaint as dogs.