Not to mention the Beta Mag the MG36 uses is reported to have had reliability problems with the M16 or M4 in Afghanistan, including one that went down and may have gotten a guy killed? The German Army just adopted H&K's MG43 as the MG4, very similar to our M249 to fill their own SAW role... the MG36 doesn't quite cut it compared to a real machinegun.
The military slings weapons when they need a hand. The only time I've ever seen carrying handles used was mass transport of rifles (took 12 M16s myself at once this way, three in each hand and the rest slung back or front) in basic, but I could have slung all of them just as easy. And with the new tactical slings, the carrying handle has basically no use for a rifle.
Machinegun, yes, rifle, no. That's why the Marines went to the A4. They want optics, and the carrying handle is so rarely used it's not even funny. I've known enough infantrymen to know.