Despite the predictable dismissals of this as mere paranoia, it's actually a very good point. As events in the last couple years have shown, virtually everything transmitted via any electronic medium, is stored somewhere........forever.
We've also found out the the feds have not been destroying the info from all those point-of-purchase background checks, as the law requires (was ANYONE really surprised??)
Once you post a make,model and ser# on the web, it's there forever, should they ever want to dig into your internet activity history.
Now, I realize if any of us are being scrutinized to that degree, we've probably already been tazed and hog-tied on the living room floor, so it's probably a moot point , but still, there's just no upside whatsover in permanently advertising full serial numbers. You can always go rent billboard space if you're so compelled, but you can't ever take it back.
And believe it or not, at some point, they really are coming for them.