Hmmm, I was lead to believe by the account I read, by someone who used one in Vietnam at least a little, and had tried out many other guns of other designs, was that the M60 was uniquely lacking in not having a handle off the barrel. He was focusing on the "get the barrel off" without a mitten problem ... ah, and depending on where he and his friends were in Vietnam setting a fire was less of a danger. But I do see your point.
OK, I've looked up the source (http://www.amazon.com/Testing-The-War-Weapons-Machine/dp/087...); this was a problem with early ones. "A friend of mine burned his hands to the bone pulling out the barrel of an M60 with his bare hands when the North Vietnamese infantry attempted to overrun his position in South Vietnam. He did not feel it at the time, but after the battle was over, he discovered the condition of his hands." They did add a handle later, and it sounds like by the time you tried one (and probably when I would have, if eyesight hadn't kept me out of the military).
Other points: Early ones had fixed front sights on the barrel.... Then he gets into reliability, and notes machine guns fire a lot more rounds than pistols and rifles. Some crazy guy put 10,000 rounds through a MG3 in 7.5 minutes, and 500,000 (!) through a FN MAG in one sitting. Obviously the soft sear is an issue there. He also says "a number of parts" can be put in backwards. Then he gets into ergonomics, the weight of the tripod (more than the less complicated one for the MG3, which also isn't made out of lightweight metal), the original bipod being barrel mounted (!!!) ... yep, your summation of it being a dog sounds spot on.
OK, I've looked up the source (http://www.amazon.com/Testing-The-War-Weapons-Machine/dp/087...); this was a problem with early ones. "A friend of mine burned his hands to the bone pulling out the barrel of an M60 with his bare hands when the North Vietnamese infantry attempted to overrun his position in South Vietnam. He did not feel it at the time, but after the battle was over, he discovered the condition of his hands." They did add a handle later, and it sounds like by the time you tried one (and probably when I would have, if eyesight hadn't kept me out of the military).
Other points: Early ones had fixed front sights on the barrel.... Then he gets into reliability, and notes machine guns fire a lot more rounds than pistols and rifles. Some crazy guy put 10,000 rounds through a MG3 in 7.5 minutes, and 500,000 (!) through a FN MAG in one sitting. Obviously the soft sear is an issue there. He also says "a number of parts" can be put in backwards. Then he gets into ergonomics, the weight of the tripod (more than the less complicated one for the MG3, which also isn't made out of lightweight metal), the original bipod being barrel mounted (!!!) ... yep, your summation of it being a dog sounds spot on.