IMO, this post betrays both a biased assumption -- that real reason anyone would buy an AR-pattern rifle is a desire to kill others, with varmint management as an excuse, and an ignorance -- that bears would fall under varmint management.
I'll address the latter first. The wildlife that tends to be classified as varmints, prairie dogs, rabbits, possums, raccoons, coyotes, wild hogs etc, all tend to have less body mass than humans. Any intermediate cartridge is sufficient. Any common handgun cartridge would probably also be sufficient, though there are at least two problems with the that: 1. A handgun cartridge may not have enough power to quickly drop larger varmints like coyotes or hogs. 2. And even out of something like a pistol-caliber carbine (think an AR or similar compact rifle chambered for pistol rounds) handgun rounds tend to be limited in their practical effective range compared intermediate cartridges. This forces one to get closer to the varmint in question to take the shot. For smaller varmints, like prairie dogs or rabbits, this means that they bolt away and you won't be able to take the shot. For larger varmints, like raccoons, coyotes, or hogs, this means that the critter might decide it's sick of your shit and attack. You might not think it, given the relative size between raccoons and humans, but raccoons can punch well above their weight and absolutely can cause significant injuries to a human.
All of the critters above tend to top-out at body masses less than a human. Compare bears, which can equal the body mass of a human as juveniles, and tend to top out at body masses well in excess thereof. If you shot a bear with an intermediate cartridge and didn't have the luck to have your first shot be a lethal one, you have now wounded, and angered, the bear. You thought raccoons or hogs were dangerous when pissed off.
Now for motivation -- that the real reason to own an AR-pattern rifle is to have something very suitable for killing people. Um, I don't know how to break this to you, but just about any common handgun cartridge bigger than .32 ACP is very suitable for killing people, this is not something unique or special about an AR-15. But I won't pretend that it isn't quite capable of such -- it absolutely is. Were I to find myself in a home defense situation, I would reach for an AR over a handgun or shotgun -- more power than the former, and more precise than the latter. I'm not going to pretend that such is any more likely a scenario than a global plague disrupting food supply chains. But, I suppose keeping a few weeks of water, food and batteries on hand also makes me an irrational weirdo.
Finally, you may have heard the phrase, "all interesting behavior is overdetermined". With regards to the large market for AR-pattern rifles, this means that for any one AR owner, they will have one or more of a myriad of reasons to own an AR -- including as a raised middle finger to those who would wring their hands about the AR's unique suitability for murder and that its ownership should be banned or restricted. For good or for ill, open defiance of overbearing busybodies has been a part of the American psyche for a long time.