Using DNA hashing as a way to identify individuals?

This is something tangential I've developed for my science-fantasy world with intelligent animals. For context: In this world, different taxonomic governments represent groups of related species. You have the Felines, Vulpines, Rodents, Avians, etc. Each of them technically belong to a different State but frequently intermingle and live in the same area, and taxonomic governments tend to also have territory/land associated with them where they primarily control the area, but other animals can and very much do still live there. Taxonomic governments have jurisdiction of the species within their scope no matter where they live, and are the ones responsible for having an ID system that works both within their own taxon and with other taxonomic governments and other official organizations.

Instead of making everyone carry ID cards or passports, which would be cumbersome for four-legged or winged animals to use, I envisioned a DNA-based ID system. The tech for this is definitely in the Star Trek levels of sci-fi, but it's basically a flat surface that you press your paw, wing, or other body part firmly onto, and a mechanism below produces a mild energy beam through your fur and skin which interacts with DNA in your cells and gives returns based on the specific sequence, and it's a safe, non-invasive DNA sequencer that can get a full read of your genetic code in seconds. The DNA scanner also checks for things like active metabolism and DNA synthesis and are generally configured to not even attempt to scan non-living cells, so you can't do something like use someone else's severed paw to make the system think you're them.

But since your full DNA sequences can be, for one, several gigabytes long and not conducive to things like printing onto certificates and migration papers or even just sending over the network to other agencies, and also contain actual information about things like your species, sex, family history and a bunch of sensitive stuff that you wouldn't want just anyone having access to, they typically take a cryptographic hash of the DNA and use that as an identifier for an individual animal. Kind of like how humans might have something like a social security number, animals in this world have a DNA Hash that governments use to identify them. Whenever a government agency in our world asks you to show some kind of ID like a driver's license, passport, health card, etc, they just have to scan their DNA and their information is automatically pulled from the right agency, using the hash to look it up. Even things like crossing international borders (of friendly nations) can be done with just a single biometric scan with no passport or ID card required. Basically, if you're animal in this world, the various government agencies around you refer to you as something like "8ed254569e8ddccea1784f569609aa32ced2691e2d22e99583ebd426cac76bd8" which is derived from your DNA sequence, and since you can't change your DNA, the same hash algorithm will always produce the same identifier, but better for privacy since it's impossible to reverse the algorithm and derive the original DNA sequence from the hash, and in theory only your own taxonomic government would have your full DNA sequence stored away on a server somewhere. Also extremely hard to falsify since it's literally identifying your body and not a card or anything that can be replaced.

What do you think? Does a system like this make sense? Are there glaring logistical or security issues that I'm not seeing? (Beyond just having a non-invasive and rapid DNA sequencing system in the first place, but that's what sci-fi handwaving is for.) Do you think a system like this is actually superior compared to physical ID media?