It's a great idea, in theory, but it's opened up a world where the possibility of scam registries can exist.
I've considered the challenges of an open and public registry, but allowing the public to access it is problematic as there is no way to validate the entries and you would be handling people's contact information. It might be an actual use of a distributed blockchain / public ledger.
The simplest way to do this would be to use the random data for an EC25519 private key, which would be used to encrypt the data[1] and then sign the encrypted blob plus an unencrypted timestamp. The registry would be a mapping of public keys to encrypted records. Updates could be accomplished by sending a record with a greater timestamp, which would then be propagated to other nodes.
You could also put a DHT on top of that to minimize storage requirements, perhaps also a PoW scheme for sibil resistance.
[1] EC doesn't technically do encryption, but that can be worked around by attaching a public key for an ephemeral keypair for your message, doing a DH against the two keypairs, and using the resulting secret as a key for symmetric encryption.
Single resource. Any vet/shelter/guy with a RFID scanner can report found pet with this barcode at approximately this location. If you know this pet, contact us here. Presumably only vets and shelters would be adding to the database, so all of the contact information is already public. People who have lost their pets can then monitor this location/sign up for alerts after you lose Fluffy.
Not as great as being able to immediately lookup the owner, but eliminates some privacy concerns.
That is, unfortunately, correct ^^^ I went through this with my dog. I was told to find out which services your local animal control and humane society use, and make sure your pet is added to those registries. Yes, some charge $$$, but the registries recommended to me were free.
If your pet ends up with animal control, and they can't find the chip registration, getting your pet back can be a nightmare.