No-flash photography is great because pictures will reflect how the environment actually looked in reality. Using a flash will wash away the mood of the original scene.
Take a look at the photo I took last weekend at a birthday party:
Prerequisite to shoot in such low-light environments is a lens with a large aperture. Fixed focal length lenses are excellent choices, like my 35 mm f/1.8 lens costing only 189$. Doing the same with zoom lenses is virtually impossible, even with the 1000$+ f/2.8 zooms.
Note that shooting pictures of people was impossible without flash. A shutter speed of 1/30 s is fast enough to avoid motion blur by involuntary movements of the hands, it’s way too slow to avoid motion blur by moving people.