Well, nice thought and good topic.
I enjoyed reading it. But I have to say that street photography cannot be classified in just 5 categories. Either you have to more as Jacques Philippe also mentioned for example, or it’s 2 kinds- Spontaneous or planned.
Or you can classify with people as subject or people not as subject.
Or… It’s just one kind. You go on street, you do photography. That is street photography.
This is my personal opinion, you don’t have to agree with that. But if you do so then thank you.