Again, it's not that straightforward. The ATF has ruled that most common rifle rounds such as 5.56, 7.62 NATO, and 7.62x39 are actually considered pistol rounds, and thus subject to AP regulations, because someone somewhere has detached the stock from their rifle, thus converting it to a "pistol".
That's... not really how that works. The US has tens of thousands of laws related to guns, and they intersect in different ways in different jurisdictions. Federally, though, at any rate, AP ammunition is only illegal for /handguns/. For rifles, there is no such legal restriction and steel core rifle rounds are commonplace. Most hunting is done with shotguns and rifles, you can easily find steel pellet shotgun shells.
The bigger issues is 1) Increased costs 2) Different ballistic performance.