I will do a main post on beginner and small operations queen rearing in the next week or so.  No cutting of comb required. 
I have grafted thousand of queens over the years. But like you don't recommend it to anyone with less than 100 hives. Then only if they want to be stock producers.

 Over the years of mentoring not being clear with terms has lead to much confusion among inexperienced and not vary knowledgeable beekeepers like yourself. We as mentors take it for granted that because the term seems so simple that all should know. Forgetting that it took years to overcome our own confusion of terms. You did make a nuc with the old queen. She will recover to a full size hive in short order. We do this every spring with our last years queens for sale. 

We sell shaken swarms or artificial swarms as an alternative to brood based nucs. There are disease and equipment reason for doing this. Simply put we shake the bees and add a queen in the customers box, in the position of the old hive. A full box of bees is our aiming point. Far stronger than a natural swarm. We move the brood to another yard and place on incubators. We keep the equipment that would normally gone out with.
The customer gets a natural varoa mite treatment, due to the interruption of the brood cycle. Reduced risk of accidental brood disease transmission contained in the breeders equipment and brood. 

Of course there are disadvantages. 
For the breeder there is a lot of extra work. Moving brood and equipment. Monitoring customer hives until pickup after conformation of egg laying.
For the customer. Hauling full size equipment to the breeders yard killing time for conformation of eggs.

One reason most folks go for nucs.