Can news stations show license plates on the air? In Missouri if that helps?

When you are in a public place you don't have an "expectation of privacy". This means anyone can legally film you.(or your car)

Now a TV station may choose to blur out a number plate to avoid privacy issues / complaints etc, especially if it has no bearing on the story, or there is a case before the courts (and the plate might then be evidence)

But I can sit out on the street, film cars driving past, and if anything interesting happens, send the film to a TV station. If your car happens to be driving past as the UFO lands, they don't HAVE to blur your plates.

People see other people's license plates all day long. Nothing different about seeing them on TV. Besides nobody can trace the numbers back to owners if they are not in law enforcement.

Sure, unless they're saying that the person definitely committed a crime before they were convicted. So, they could say, "This car belongs to someone ALLEGED to have robbed the bank." And if you're in public, it's considered public information.

Now, they couldn't say, "This driver robbed the bank" until that person was convicted.

If there's an Amber Alert, you can get the license number on a text by phone.

It's not like anyone can trace the owner of the car.

You bet, all legal. Only exception would be if the vehicle owner was under investigation by law enforcement or had criminal charges pending.