Can be good. As in this recent low key portrait of my friend and colleague photographer Joseph Marranca:
A low key portrait is a portrait where background and clothing are dark, and only a small part of the image is lit.
We used one small beauty dish. Straight above Joseph. And the white studio walls, because they got no light, turned dark. This is key: umbrellas would have spilled light onto the background. This small directional light allowed the background to remain dark.
(The dish failed to perform: it did not make Joseph beautiful).