The issue is having a fool proof method of linking a bike to its owner. Sure, you could present an image of the frame number, or you riding the bike, but what is stopping a bike thief from also doing that after they have had the bike for a day or two?
Receipts aren't designed for proof of ownership over a long period of time, and as such they are made of cheap materials and inks. I have a receipt from August 2011 in my wallet, and already the ink has rubbed off to near-unreadable.
I believe that for this to work effectively, there would need to be a mandatory centralized government run ownership system, similar to that of cars - But then of course we have a whole new range of inconveniences, with displaying tax discs/sticker equivalents, and ownership transfer etc.