I'm not even kidding here, a vet that would actually recommend AGAINST testing a diabetic cats blood sugar, would cause me to switch vets. That just shows a serious lack of knowledge on the subject.
It would be akin to a doctor recommending that a diabetic person just ignore their blood sugar because it's not necessary. It's actually DANGEROUS blind dose insulin. What if the cats blood sugar is already fairly low when you dose? Then you end up with HYPOglycemia. Blood sugar drops drastically and the cat ends up passed out and needs a trip to the vet. I've seen this with both animals and humans. It's why you see diabetics carry around candy with sugar just in case their blood sugar drops too low. A friend of my dad had a son who was diabetic from a very young age, and hypoglycemia was always a strong concern. Blood testing was constant and necessary and carrying something with a high sugar content to offset that issue was a must.
The fact that the vet sees no link between food and managing diabetes is also worrisome. Even with diabetic people a diet low in simple carbohydrates and sugars is recommended. It's the same with cats.
I would definitely try to find another vet that's will be willing to work with the owner more closely and knows more about managing diabetes. It sounds like this vet is just going to be working AGAINST you guys, which at best is going to cause frustration between owner and vet, and not good for everyone's mental state, not to mention not helpful with managing the cats condition.