This is a very interesting question you pose, and I'm not sure of the answer.
I guess the first "other" sport that comes to my mind which works the way you mention (optional classes, otherwise mentoring) would be climbing, which shows a lot of parallels to diving: You need to know some equipment and certain basic skills in order to keep yourself and your partner alive and well; it is a reasonable safe sport at "recreational" levels, but becomes progressively more risky when you leave this area; While someone can teach you certain skills, the feeling for it and the mastering of those skills only come through experience. I'm sure there are more.
So - as I said, I can't answer the question for myself, at the moment I can't see why diving should be different from climbing with regards to instruction, but I'm open for pointers as to what I may be missing.