Which caliber is "perfect" for the AR depends on what you're using it for.
If you're using it for 600m target shooting, .308 is a good choice.
If you're hunting coyotes (assuming it is legal to do so), .204 ruger would be perfect.
If you're plinking, .22lr is the perfect choice
If you're hunting whitetail deer, 6.8SPC would be perfect (again, assuming it is legal to do so)
If you're competing in a service rifle competition, 5.56 (or .223) would be perfect
So there is no single answer to your question. It's like asking "What is the perfect gun?" A Glock 22 might be the perfect gun if you are using it for self defense, but it would be a terrible choice for trap shooting.
A better question would be "What is the perfect caliber for __________ with an AR?" (and you replace the blank with the specific activity you will be doing).
So with that in mind, every caliber is perfect for something, so I chose every one.