If any instructor, or student, feels training can go beyond the minimum standards then by all means go for it. Of course this would be between both parties and with utmost safety. There was only 2 in my OW class and both of us were very equal in ability and advanced very easily and quickly. With our okay the instructor did a bit more. For example our last dive for certification we went to 80ft on a wreck and did a swim through. I used the same dive shop for AOW but a different instructor. They both worked there a long time and knew each other. The other student moved on and when I came back my OW instructor passed on info to my AOW instructor. I think they conspired to drowned me. Anyway we were 1 on 1 and she really put me to the test. I enjoyed the challenge and it made me a better diver right out of the gate. My confidence was high and I have enjoyed compliments from many dive masters ever since.
I also don’t think it matters what agency, it should be between instructor and student. An instructor should guard against being too rigid and just run through the basics. With a sport that demands good training skill levels should be scrutinized as soon as you jump in the pool.