Lovely idea, but I don't think it's a lack of serial numbers that makes it easy to steal a bike... My bikes all come with frame numbers that I have linked to the property vault (I even have my Fox Fork serial number on there).
I have thought about this in the past - bike registration through the government like we register our cars. That way bikes that are sold registered can be tracked back to the original owner, registered bikes hold better value, everything is transparent and goes through an official channel when changing hands (no more buying a TRAK MTB from a dodgy dude in a McDonalds carpark after dark) - BUT this comes with a myriad of other issues...