Perhaps you want to capture both an aesthetically beautiful image and document a scene, and of course that's possible. Life on the streets often does have a beauty about it, and individuals certainly do. You might reflect that beauty in a portrait or a cityscape. What I'm talking about here though is seeking a beautiful or striking composition - the balances of light and shade and color, the patterns and textures and repeating elements. Is that more important than telling the story that's in front of you, more important than documenting the scene or event?
Eugène Atget, the early french documentary photographer, was notable in his determination to document his surroundings as he found them, particularly his city of Paris. His work caught the interest of other artists such as Man Ray and Picasso, but he rarely if ever considered himself an artist, famously replying to Man Ray when asked if he could use one of Atget's images: "Don't put my name on it. These are simply documents I make". Berenice Abbott, the American photographer who helped promote Atget's work, called Atget an 'urbanist historian' whilst also noting his deep love for the city of Paris whose images he was recording.
Henri Cartier-Bresson, perhaps the most famous street photographer, was often more concerned with aesthetics. He played with light and shade to create the shapes he wanted to give an artistic composition. Whilst he became well known for his concept of the 'decisive moment' (capturing an event just at the critical moment), he was also a painter and heavily influenced by the surrealist movement.
There's no right or wrong approach and maybe we all tend more towards one approach than the other. Atget was still very much an artist, and Cartier-Bresson also documented what he saw. It's worth being aware of your own preferences and intentions though, and you may choose to seek one over the other on a specific day or for a specific project.
And when the two converge for that perfect moment, then you might just have real magic.