Well, once you know some of the rationale behind single-person katas, you can work some things out for yourself. They are really meant for you to find out for yourself what's there by doing them and thinking about the purpose of the movements.
There is so much the master can tell you, but the art is for you to work it out for yourself. If you take a good kata and work on it by yourself for ten years, really diligently, you'll develop your own understanding. Of course, that's assuming you do kihon practice and kumite along with the kata practice.
Best to all.
I suppose there is some value in this, but for me, I prefer a much more direct and "open book" approach to spending my time training. My instructors can tell me everything that they can tell me, the day I am better than them, or their is nothing else they can provide, then I am moving on, as it should be.
I agree that you have to work things out for yourself at some level. In BJJ circles the masters talk about "developing your game".
However, I think this might be a slight bit different based on your description above, as they teach with an open book and tell you what things are and what they are designed to do. Developing your game is not about that, it is about synthesizing the practice into patterns and responses that work for you.
So any single person kata I do is about developing structure and conditioning. Sure some of the motions might look like something you'd do in fighitnig, however it is very clear that they are about conditioning and development...not about finding hidden bunkai. My teachers can and do tell you why we are going what we are doing.