Surely you could say the same about landscape photography or macro photography or wildlife photography ?
You wouldnt go out with a 50mm prime lens and expect to shoot wonderful nature shots for example. You might get a few by luck, but in general it wouldnt be the lens of choice for that application.
I would consider myself a street photographer, not because I take loads of pictures of people in streets but because I shoot whats there, there is no set up, no lighting, no posing and I dont know many of the people I shoot, I just shoot what I see.
For me what makes a good street photographer is the ability to capture a person(s) doing something interesting, that may be an action, it may be something as simple as a facial expression or the interaction between two people but the image has got to have something, just taking pictures of people in streets offers nothing.
The other 'rule' if you like is to be discreet so big zoom lenses are not advisable, people soon clock on to the fact that you are taking a picture of them when something resembling the barrel of tank gets pointed at them.
In the same way I never use flash, because nothing draws attention to yourself like a flash going off.
So I use fast prime lenses, Canon 35mm F2 and Canon 50mm F1.8