Nonsense.
You're going to end up handing over the VIN anyway so, the Carfax, if one is desired, will be run one way or another.
I pixelate license plates. Every little bit helps online.
It looks terrible to use one's thumb, though. When I see that I skip right by, because if the idiot isn't bright enough to at least just tape a piece of paper over it, I don't want his car.
Why not take it off? Some people will suspect the car has been sitting and will never call, as a result. On that subject, a burner phone is a good idea on Craigslist.
Cheers,
Kennith