Every time there's been a demonstration of this sort of technology, it has failed. The one time it didn't, it was quickly revealed that the only reason it worked is because it had been disabled -- that is, it was just a regular gun going bang.
Biometrics are great in a controlled environment, but you're talking about a gun. Maybe a rifle, maybe a handgun. Maybe it's a hunting rifle, and maybe it's covered in snow. Or sand. Or mud. Maybe the hand holding it is wearing a glove. Or is covered in sweat.
It's not *reliable*. Making a gun *NOT* go bang, that's easy. Making it go bang every time you want it to, that's the hard part. Making it go bang every time you want it to, but *never* when you don't? That is impossible. Shit, even with some pretty clever mechanical safety mechanisms on guns, people still wind up getting shot accidentally. They could be made more robust, but then the gun would likely fail to function when needed.
The solution then, is to use those mechanical safeties, but to not *rely* on them, because the gun might still go bang.
This sort of tech, though? You can't use it but not rely on it -- if you are using it, you MUST rely on it, or else the gun WON'T go bang. Unless it does because of some sort of breakage or something, which can happen. That's why you never point a gun at something you don't intend to shoot.
There was tech that involved bracelets or rings with RFID tags, but those were useless. Again, they didn't work when tested, and even if they had.. the purported purpose was to be for law enforcement, to prevent criminals from stealing their sidearms and using them against the cop (.. that's really a problem large enough to justify replacing millions and millions of dollars in sidearms apparently (it actually isnt.)). Except the tags either worked from too great a distance -- so that it wouldn't prevent the gun from firing if the ring was within a few feet -- or just didn't work 100% of the time because the distance was too small, and a little interference meant the cop pulling the trigger was in for a surprise.
There was also a bill I believe around the early 00s out in California to require bullets to be microstamped *BY THE BARREL OF THE GUN THEY WERE SHOT FROM*. Yeah, the bill sponsors even had a company out there who had "perfected the technology" that everyone sane knew was impossible. Turns out the company was, in fact, impossible. Just an empty office in an industrial complex somewhere, nothing more. There wasn't ever any big investigation, it just sort of went away, but that's the kind of bullshit that goes on here. Politicians and their allies (fwiw i personally think that shell company was set up by the brady campaign /tinfoilhat) will create a fake company, have that fake company put out fake claims, and use those fake claims to de-facto ban guns because that fake technology doesn't exist. Eventually it would be sorted out, sure, but in the meanwhile NO GUNS FOR ANYONE!