The AR platform's direct impingement operating principle has a far greater accuracy potential than the AK or FAL's gas piston (or a piston AR, for that matter). DI is probably the best operating principle for building a supremely accurate semi-automatic rifle. That's why the M110 system is an AR, not just an updated M14.
However, for the next generation of infantry rifles, you're seeing nothing but gas piston systems. Modern piston accuracy is "good enough" for the engagement distances that modern infantry units encounter. Modern DI rifles are "reliable enough" for the field conditions that trained, equipped first-world militaries operate under.
However, I'm not a trained, equipped first-world military. I'm some random dude who'd rather spend more time shooting and less time cleaning. A gas piston rifle is much more tolerant of bad hygiene and maintenance than a DI rifle, and my FAL is still more accurate than I am from field positions.
An AK isn't - I shoot better than even the nice Bulgarian AK-74s or converted Saigas. Most FALs are 3-4 MOA guns, and I'm about a 2-3 MOA shooter, depending on the day. But without an extremely steady rest like you see at Camp Perry, my FAL is more than accurate enough for my shooting.