I use to teach full stop taxi backs and then use the taxi time to debrief the previous circuit, however later I found it more effective to teach touch and goes as this way we could get more circuits in. In order to reduce the workload for my students I would take control after they landed and then take off myself, using the initial climb to debrief the student on the previous circuit and landing. Later when they became more experienced I would get them to do the takeoff as well.
When it came close to them going solo I would then start teaching full stop taxi backs as this is what they would be doing by themselves. I found this system worked quite well and most of my students learned at a faster pace than most.
Students should be getting comfortable with the take-off from exercise 9 onwards because they have been doing it since probably 6B. AT somewhere like Bournemouth, the student lands the instructor re-configures and when told to, the student applies power for take-off and does what they have been doing several times before.
The only time I would stop and taxi-back is if they are having problems and we need some quiet time or we are going to do something like a short or soft field take-off exercise. However, since they can be done on the first take-off, the need for stop and taxi-back displays a bit of a problem in deciding the order of trainig to avoid unnecessary breaks.
using the initial climb to debrief the student on the previous circuit and landing
What do you teach that student about the critical aspect of the initial climb? - teach as you do and do as you teach.
The aeroplane is for practice. The value of talking in the aircraft while moving is 10% of the value obtained by doing the same brief in a quiet room.
The taxi is recognised as being one of the more critical parts of a flight but this is often ignored. Don't speak of items unrelated to taxi unless the aircraft is stopped - teach as you do and do as you teach.
The 12/13 exercise must be built in stages but ther take-off should be taught in small stages starting with exercise 4A - demo, 4B - follow through, 6A, 6B, 7/8, 9, 10A, 10B, 11A practice........At a minimum they should have done 5 take-offs before they start 12/13. Thus the keeping straight, rotation, climb attitude and climb should already be covered and simply needing polish.
They also need to be able to climb, descend (7/8) turn and climbing/descending turn (9) and fly straight and level (6) because they have already completed those exercises.
Therefore leaving the flare and landing out, what is new in the circuit beyond the quickfire repetition (learning by rote) of basic handling skills previously learned?
If the student can't fly the circuit then the instructor has failed to teach them exercises 1 to 11.
If the student needs a further brief in the air then end the exercise and do the brief. Don't waste their money since they are going to associate you getting some free flying (while mouthing off about something that they clearly do not understand) with them not making progress and put 1 and 2 together to get 3.