It's more than weapons cleaning, any modern infantry machinegun will fail if fired relentlessly, belt after belt. In the hands of a single gunner, they are designed for burst firing, generally 6-8 rounds at a time with a few longer ones as necessary, and if clean at the start and lubed appropriately for the environment, they will normally go a couple of thousand rounds before excess carbon build-up in the moving parts within the receiver or gas tube becomes a huge problem. They aren't designed to deliver sustained and uninterrupted fire belt after belt for 2000 rounds. Just because you are in a static position with thousands of rounds of ammo laid by does not mean the gun will continue to work until all the ammo is used up. It requires fire discipline, not mad-minute shooting for half an hour. The guns can sustain that kind of heavy fire only if handled as a true crew-served weapon, making the necessary barrel changes and ideally having two guns covering the same lanes or even in the same bunker to cover each other's down time.
The SAW's major jamming issues occur when trying to use rifle mags in it, the capability was part of the spec but it doesn't work all that well, it's sort of a last resort (Still, better to try it than be overrun, or try to beat someone to death with an empty SAW); they are pretty reliable feeders using belts or assault packs (Which are packaged belts).
The three-round burst is a good feature if used correctly; 'Correctly' normally means at targets closing on you (Or you on the target) at under 100 meters, because beyond that you are either (1) aiming and hitting with the first shot and generally wasting the other two, or (2) just wasting three rounds because you didn't even aim the first one.
