In studio photography, you want to kill ambient light completely. The light bulbs in your studio, or the light falling in through the window, should not affect the picture at all.
This is easy when using flash. 100 ISO, 1/125 second, f/8 and you’re all good. Ambient light: gone.
But when you are using hotlights, it’s not so simple—especially if you are using small, light, and affordable compact fluorescent lights. These are (by definition!) exactly as bright as a lightbulb. So now you need higher ISO, longer shutter, lower f-number… and now your lightbulbs do suddenly show up in the photos.
And that’s why most photographers use flashes.