1. Legal full auto ownership only applies to guns made before 1987. The FN P90 you showed was invented well after; it is illegal for a civilian to own. (Were it legal, I’d own one.)
2. I spoke of pistol caliber carbines in general, not just of 9mm. Your “alternative” is a pistol round, interesting only insofar as it is optimized for full auto use, and subsequently uninteresting because the gun optimized for it is illegal for civilian ownership. The 5.7 pistol is only seriously considered if the operator has a P90 as primary; few would seriously use it on its own. The PS90 (of note normally built with a >16” barrel) is a stunted & overgrown version of the laudable P90; if you’re going to have a semiautomatic that size, feed it serious ammunition (.223Rem or .300BLK at minimum).
In colloquial discussion, people use the term “firearm” in ways broader than 26 USC 5845. Yes I am aware of the variations of the legal definitions of “firearm” (having written opinions on applicability of NY weapons laws which are used by police as guidance), but do not expect most others to know and follow them exactly. I doubt your grasp of such laws, considering your apparent ignorance of 922(o).
I politely welcome any correction of misinformation.
A pistol is used to fight your way back to the rifle you shouldn’t have left.
When you reach that rifle, it shouldn’t be firing the same paltry ammo.
So your a lawyer?