Fouling from the gas system has not been a significant failure mode since powders were switched in the 1960s.
The real problem with the AR/M-16 platform is based on the magazine. Cheap aluminum magazines made by a rotating cycle of minority bidders makes for a very unreliable feeding system.
I've been shooting ARs and M-16s for over twenty years and even after THOUSANDS of rounds though my rifles in single sessions, I've never experienced a carbon-induced failure. It's always been the mags and now that the AWB has expired, we're seeing a much higher quality of magazine (HK steel, new stainless mags, and soon a new polymer mag) than ever before.
While that's an excellent point, the mags used in the military are often old, worn, and prone to failure. Also, many units don't teach troops how to clean magazines, and keep reusing bad ones.