The Army manual is written that way to keep people who don't know what they're doing from trying to mess around with their weapons. The KISS principle has to be factored in as well, it does simplify training when all you have to teach is basic marksmanship and routine maintenance. Most average soldiers (particularly those who are not a combat MOS) probably don't know what headspace is, let alone how to check or adjust it.
Another admonition that makes sense is that you are not supposed to mess with the trigger group in a M16A2, people have reassembled 3-round burst trigger components incorrectly before and ended up with a runaway gun.
The Army's opinion is that any weapon maintenance beyond regular cleaning should be left to armorers. Those sustained fire rates are deliberately set low to provide a margin of safety to the soldier and to increase weapon system life.
In short, the Army writes things the way they do because they have to worry about Murphy, in addition to concerns about Joe trying to do things he's not qualified to do.
There's plenty of people in the military who are issued weapons and aren't "gun people" and therefore only know what they've been told by Uncle Sam. For that matter, there are a good portion of people in the military who are not warriors and/or are not in a combat MOS, I'm sure a lot of the guys here know what I'm talking about.
Oh, and IIRC, the M16A1 uses a lighter bolt/bolt carrier than the M16A2 and later variants, but I may be wrong.