The ATF has banned armor piercing rounds specifically for that reason, but they also have a (17 page!) document listing how, when, and why certain armor piercing rounds fall under a "sporting exception".
https://www.atf.gov/firearms/docs/general-notice/armor-piercing-ammunition
"Specifically, the definition of “armor piercing ammunition” in 18 U.S.C. 921(a)(17)(B) provides:
(B) The term “armor piercing ammunition” means—
(i) a projectile or projectile core which may be used in a handgun and
which is constructed entirely (excluding the presence of traces of other
substances) from one or a combination of tungsten alloys, steel, iron,
brass, bronze, beryllium copper or depleted uranium; or
(ii) a full jacketed projectile larger than .22 caliber designed and intended
for use in a handgun and whose jacket has a weight of more than 25
percent of the total weight of the projectile."
It would appear the ban was intended to restrict the sale of what the press hysterically called "Cop Killer Bullets" back then. Phrase was all the rage. No mention of rifle rounds, only handgun rounds, and rifle rounds would later be explicitly allowed by the ATF:
"Between 1986 and 2011, ATF received few exemption requests for armor piercing
ammunition. In 1986, ATF exempted 5.56 mm (.223) SS109 and M855 “green tip” ammunition
containing a steel core. Similarly, in 1992, ATF exempted .30-06 M2AP cartridges. Since 2011,
however, ATF has received approximately 30 exemption requests for armor piercing
ammunition. Several developments since 1992 have spurred the influx of exemption requests.
ATF understands that one of the primary factors is the increased pressure on the ammunition industry to produce suitable hunting alternatives to lead ammunition. The widespread use of lead ammunition for hunting has been linked to lead contamination in certain species that consume carrion and “gut piles” containing remnants of lead projectiles. The endangered California Condor, which scavenges on carrion, has proven particularly vulnerable to this type of lead poisoning. The impact of lead poisoning on the Condor and other species has resulted in at least one State banning the use of lead ammunition in certain environmentally sensitive areas, and has generated substantial advocacy for broader availability of non-lead ammunition. Generally, rifles are the type of firearm predominately used for hunting purposes, particularly the type of hunting conducted in sensitive environmental areas such as the California Condor range. It thus appears that rifle-based hunting is the primary driving force behind the market demand for lead-alternative ammunition made with the metals listed in section 921(a)(17)(C)."
Oh, man, I had TOTALLY not considered that angle. Yeah, as states ban lead ammunition, that's going to spur development of alternatives which would ordinarily fall under the armor piercing definition unless they are granted a sporting exception.
I wonder if the "straight wall" ammo requirements had a similar impact?
https://www.remington.com/big-green-blog/what-states-can-you-hunt-with-a-straight-all-cartridge.html