Why is it that when a news crew interviews someone, the camera alternates between showing the person's front face and showing the person's face from the side while they're talking??? I always crack up when they do that. A couple of times I've even seen them cut to a ceiling cam for a few seconds! And the guy's just sitting there continuing to talk facing the original camera like nothing is going on! And I'm thinking "Uh what's the point of them doing that????"

Usually there's only one camera. They record the interview continuously with the camera on the subject. Then they shoot the reporter (re)asking questions and get some shots of the subject from different angles. This allows them to edit the subject's answers without the cuts being obvious. The edits may or may not do justice to the original comments.

Politicians and big business types with PR flacks will often make their own recording of the interview so if the TV people twist things in editing they can release what they actually said.

Radio I think you're talking about one of those multiple-camera interviews where they use non-traditional cutaway shots of the subject instead of staying with the normal close-up or medium shot. Sometimes one of the shots will be in black and white and other times an overhead or wideview angle reveals all the light and camera set-ups. Its kind of MTV-documentary style?
That's somebody trying to be film-school creative and keep the interview more visually interesting and like Fred said its to cut together parts of the interview without having a jump cut.

I agree that its awkward and artificial but at some point somebody thought it was cool. Cutting in b-roll (scene video) instead of a bunch of weirdo camera angles would be a perfered option.

That overhead shot business is dumb. I saw one of those shots done with a convex mirror like from a store - real cheese-ball stuff.

Its very rare to have a multi camera interview for a local news story. 60 Minutes/Dateline/20 20 would do a 2 camera shoot.

You may also have a fixed camera with no one attending and a camera with a camera man.

Then there is the stationary camera where the guy setting it up is also the talent....