@Gary_H I think to answer your question you have to look at a couple of scenarios.
Yes the SBR stamp is assigned to ONE receiver. If as @Enzo_T points out you filled out the paperwork to encompass a variety of lengths and calibers you would be good. Yes there are restrictions and hoops to jump through to cross state lines (a closer look at the caveats is in order )
NOW the point of contention comes in, if you should be one of those lucky enough to have an SBR and a regular old AR-15 and they happen to be in the same place at the same time you COULD be in"Constructive Possession" of an unlicensed NFA weapon. In that, should you get your lowers mixed up, you COULD put the 7.5" tube on the rifle lower and therefore be in violation. Not that you would, Not that you did, BUT YOU COULD. This is a similar rabbit hole that the ATF has used to prosecute a felon that lives with an non felon that owns a gun.
I do not have a good answer as to how to fix that issue. Similarly if I have a barrel wrench and vice blocks and a 7.5" tube am I in “Constructive Possession” just to OWN a 7.5" or 10.5" or 14" tube and gas parts? Further down that rabbit hole, if I have my SBR and my buddy brings over his “regular” AR-15 are we BOTH in violation. As you mention they can be swapped out faster than changing under britches. Further down the rabbit hole would leave all of those with a pistol and a rifle in “Constructive Possession” because of what we COULD do and that is before we start talking multiple uppers and different calibers. The lid is being lifted on Pandora’s Box and it ain’t pretty for AR owners.