It comes down to privacy.
For $30-$50, I can run anyone's plate (
http://www.licenseplate.net/38_state_vehicle_plate/index.html). And that doesn't count the criminals that have connections to people at the DMV/Law Enforcement (they do for a reason). I have access to TxDot here, which allows me to run any plate (tx only of course), any time and it reveals a treasure trove of information about the individual. I'm sure there's people in every state with the same access.
Criminals can also use your plate number when they have a similar car, then when they commit the crime, guess who shows up in the searches?
Another aspect is that it can link you or incriminate you in a crime. I'm sure it's been posted on here that someone has "driven above the speed limit" occasionally. If I was someone's lawyer and I was able to connect a person's admission to speeding with their license plate as confirmation of identity, it's game over.
The only argument I've ever heard as to why they "don't care" about hiding their plate online is "hundreds of people see it everyday on the street." "Hundreds" is still less than potentially billions and once posted online, it becomes a "paper trail", a timestamp in history that you can't erase. It's also a lot easier to remain anonymous online than to walk up to someone's car on the street and take pictures of plates.
I could go on about privacy concerns and identity theft, but it's a simple decision. Don't mask it if it doesn't bother you. For some, who are probably a bit more privacy-conscious, it takes two seconds to black out.