Top: with flash, 50 feet to the right and 20 feet up. Bottom: no flash. Senator Hillary Clinton greets fans before speaking to several thousand supporters in Madison, Wisconsin, the day before the primary election.Basically you asked: Why?
I hope the examples above answer why. You can see the difference most on Hillary's hair and the face of the girl in the middle. The light helps Hillary stand out from the crowd, which she badly needs to do right now!
These events are often held in giant bat caves (gyms, convention halls) Even though the podium and parts of the room may be well-lit, I don't have control over it. I get cleaner light when I add my own. I prefer unobtrusive lighting, so I blend my flash with the million different light sources present (spotlights, overhead fluorescents, TV newslights, 2,000 point-and-shoot flashes.) My goal is usually to get some nice side light or rim light to separate the subjects and background.
It's true, more can go wrong when you add lighting. Batteries die. People get in the way. But to be honest, in a scrum like this, a lot of shots will fail no matter what. I hope to get a few great shots. Sometimes I succeed.
I use Pocket Wizards, which send a radio signal from my camera to my flash. I set up a small flash ahead of time, taping it to some railing or wall out of the way. Secret Service hasn't bothered me. And there is usually time to kill between security clearance and the start of the event to do it. I don't file photos as fast as people shooting for the dailies, so I have freedom to play. (Thank god.)
And tell us the geeky technical details.
The two photos above were taken less than a second apart. Too fast for my flash to recharge. Both were shot at 1600 ASA, 1/125 at F4. Canon 20D. Nikon SB26 about 50 feet away at 1/4 power. Orange gel on flash (1/2 CTS I think) to match mostly tungsten spotlights with camera set to 3700K.
Ok, I'll get off my soapbox now. You can learn much much more about using off-camera flash at strobist.com