I feel people are more likely to check Bike Register as its obviously marked & stickered than they are to check a frame number on an unmarked bike.
The Bike Register sticker serves as a deterrent to opportunists.
Only opportunists who are too dim to put another sticker over the Bike Register one (possibly another BikeRegister one?) or fence it to someone who resprays. It's a pretty good advertisement to the inexpert opportunist that you consider the bike actually worth nicking, too.
The pot is rightly or wrongly finite and shrinking and I believe that people should take some responsibility for their own goods.
I'm more concerned that the police are working for private marketing businesses like BikeRegister than that they're spending money on ink.
Because bike theft is crime, and prevention is way better - cheaper, more efficient, better for society - than letting crimes happen.
But I wouldn't expect an incompetent, nasty government to recognise that.
Prevention is stuff like catching thieves before they succeed in nicking a bike and having an architectural liaison officer responding to consultations to get cycle parking and storage made secure (instead of leaving blocks of flats with only wheelbender sheds accessible by the public), rather than wasting time writing easily-obscured numbers on bike parts that already have them.
