Yeah, I would not depend on a USEF registration as ownership documentation, because they don’t require any documentation of ownership to register. I know this because I had a lessee who registered MY horse in her name during a short term lease without my permission, and I was the one who had to provide documentation of ownership to put him back in MY name when I later found out.
Not all states inspect brands. Mine does not - they register them, but there are no brand inspections. It could deter someone from acting shady, though, and sometimes it helps identify a horse that has fallen through the cracks. And not all (probably most don’t!) auction houses scan for chips, either.
So, I suppose it depends on what kind of situation you are trying to prevent - theft vs a dispute like the ones described here, loose horse found, horse at auction, etc. I have considered numerous times that I should probably do SOMETHING to my run of the mill chestnut quarter-type pony that doesn’t have any unusual characteristics. I obviously have vet bills, and a bill of sale from when I bought him at the auction - but none of that really has appropriate info to identify one chestnut gelding from another definitively.