"If that's the case, then why do the ARs dominate so widely in so many fields?"
In what fields do they truly dominate? Are they the most common hunting rifle? Are they the most common self-defense tool? Isn't this a case of perception? It is clear you are a fan of AR's, and why not be? They can be great rifles if made by a good manufacturer (crap if made by folks like Hesse/Blackthorne). But are they the most common varmint rifle? Deer rifle?
I don't mean this as an attack towards AR kind of guys. The lever action rifle dominated the hunting scene for the first 50 years of the 20th century because it was the dominant rifle used - they were used more than any other type. After WWI, their dominance began to be chipped away by soldiers who used 1917's and 1903's during the war. Post 1950, dominance evolved to the bolt-action sporter. Today, while lever action rifles remain popular, bolt-action rifles dominate the hunting scene.
I have seen nothing that indicates an AR type has taken over any particular category beyond competition shooting, though significant inroads have been made in varmint-shooting. Police use is through the roof, so I'll agree it dominates there - displacing the riot gun.
Considering the cost of a Savage 110 with nice glass, the AR will remain more expensive for most hunting applications while not necessarily providing any better performance. High capacity magazines don't get to go to that party. Even so, an AR can't economically replace my squirrel gun, deer rifle, self-defense pistol/revolver, bird/rabbit guns. For my use, it could displace my Ruger Mini 14 GB for coyotes or rabid racoons but that is about it.
If they were so dominant, then Wal Mart would still sell them. They still sell shotguns and bolt action rifles. AR's don't move fast enough to justify keeping. Of course, that Wal Mart even began selling them is evidence of their popularity, but it was not sustainable else they'd still be on the shelves.
None of my posts are intended to disparage the AR. While it is true that, having owned a number of them in a number of configurations in the past, I have finally concluded the AR is not for me, others using them is just fine by me. I don't even have to begrudgingly give it credit - I know they can be superb rifles.
Louis Seacamp invented my personal favorite hunting rifle, the Mossberg 800, in addition to other things, but I know for a fact that his firearms contributions are steps below Browning. It's pretty easy to not own a Stoner design. Yet how many of us own and use something that comes from Browning's designs?