That's probably only half true. With that said, right now the NFA exist. No one is stating that the bird grip is better than a stock; however, within the current confines of the law, it's better than having a full sized shotgun in many instances.
I'd probably have one of each. If I could fit a SBS in a duffle or bookbag as well as use it in the same roll as a SBS, then yes, I'd opt for the SBS. That is not the case though.
I and many others have a pistol grip on their 18" shotguns which can legally have a stock on them, so I think you are wrong about the bird grip shotguns disappearing if the NFA went away. I do agree that braces, binary triggers, and bumpstocks wouldn't exist though.