“Possessing a live grenade is illegal.” https://www.criminaldefenselawyer.com/resources/criminal-def...

Obviously there’s a bunch of exceptions, including as you point out the federal option of going through a background check and paying 200$/grenade. But that’s only at the federal level it doesn’t necessarily meet state requirements.

The rules on those background checks are as capricious as banning people who were dishonorably discharged from the military.