I think it's an excellent idea, and here's why. Out where I live, there are all kinds of calls about animal abuse, usually from neighbors who see emaciated horses, goats and cattle in the field, starving dogs tied to a stake and the like. Once animal control steps in and takes charge of the animals, a report is issued. These reports should be collated so that breeders, animal shelters, livestock auctions can make a simple check of the registry to make certain they aren't selling or adopting out animals to people who have been ticketed for abuse.
For example, our local animal shelter tries to screen potential adoptive parents, but there's no way to know if that nice guy who took an entire litter of kittens really loves cats, or has a history of using kittens as bait to train fighting dogs. The cost would be minimal. A couple of people statewide to perform some routine data entry, or write software that makes entries automatically when such reports are generated.
I'm for it.