Who would need armor piercing rounds anyway other then the military or law enforcment or anyone intending to pierce armour. Here in AZ a local gun store has tons of old surplus ammo mostly steel core i guess is classified as AP ammo but its sold dirt cheap since most of it is corrosive or mildly corrosive I don't mind using mildly corrosive ammo when I'm done shooting I just swab the barrel with some hoppes number 9 and spray the bolt with rem oil. They sell some czech 7.62x54 Rimmed ( Not russian) from the 60's which is mild steel core copper jacket which when originally manufactured was never intended to be AP but the "EXPERTS" with the BATF classified it as AP.
But anyway the stuff shoots great out of my mosin nagant prints 2 inch groups at 100 yards with open sights the best part is its like 2 dollars a box of 20

Yeah its legal to own, sell, and shoot. but by law the retailer has to keep record of the sales on it. But aslong as you don't intend to do anything illegal with it you have no worries. untill the BATF decides to ban it altogether. But It is illegal to manufacture, import or export.