As photographers we shoot. We go out armed with our cameras and an empty memory card looking for a target. When we find that target we put our sights on it and shoot. And if it doesn't work out we try again. We change our angle, we change our lenses, we change the subject until we get the perfect shot but we do not stand around and just wait for something to pass by.
Simply standing on a sidewalk and waiting for something interesting to pass by is not good street photography. It's more akin to fishing without bait. Quality anglers choose a particular type of bait to attract the fish. They also use their knowledge of location and time of day to help ensure a good catch. And if they yield nothing, they change their methods. In other words, even a fisherman prepares for a fishing expedition.
There is a school of thought among those who teach street photography, that the best method of capturing the moment or people in their natural environment is to find a location with an interesting background and to just wait until someone interesting passes by. And then you simply push the button. With the advent of small mirrorless cameras and cameras with tilting LCD screens, people are further being told to hold their cameras at the hip as to avoid detection of their activities. Somehow it's more discreet. And being discreet equals more natural candid pictures of people in their natural environment and therefore good street photography in this line of thinking. This is a rather peculiar piece of advice. If you were to see someone standing on a street corner with their head down, a camera in hand, not moving from their location, would you not find the activity not only strange but perhaps alarming? And if you saw this, might you even call the police to report suspicious activities?
Good people photography is more often about engagement with the subject more so than a fleeting moment. This is not to say that every photo requires the subject to be looking at the camera. Although a subject's engagement with the photographer certainly can help, it is most helpful when the photographer engages with the action. The photographer has to be a part of the place or the thing that is being photographed, and yet not intrude on the action.
So if you are looking to create good street photography you ought to think of yourself as a hunter. Hunters find their target, set their sights, and then track the subject until they have a clear shot. And as photographers we ought to do the same.