Full disclosure, I actually like non-reciprocating charging handles as much as the next person. However, there are actually some very good reasons why most military rifles don't use them.
1. More parts make them more expensive and complicated to manufacture
2. They hide information about the state of the weapon system. Let me explain...
We have all seen either in combat or on TV the dreaded situation when the rifle jams. With the M-16, the operator has a confused look of terror as he un-shoulders the weapon and inspects the chamber. He then attempts immediate action in various sequences by frantically removing/re-inserting the magazine, pulling the charging handle, pushing the forward assist or generally just slapping the side of the weapon or banging the butt stock on the ground to make it work again.
A reciprocating charging handle on the weak eye side of the rifle provides an enormous amount of visual information and simplifies the operation of the weapon system. The operator only needs to be concerned about pulling the trigger and then pulling or pushing the charging handle. For example, in no particular order.
1. If charging handle is locked open to the rear, pull it to charge the weapon
2. If the charging handle goes all the way forward and it does not fire, recycle the charging handle
3. If the charging handle goes 2/3 of the way forward, push the charging handle forward to fully seat the round
4. If the charging handle goes 2/3 of the way forward but won't push forward, pull it back and clear the chamber
5. If the charging handle won't pull back, remove weapon from shoulder to forcefully retract bolt or mortar the rifle etc.
The point is that the operator can deal with a range of common issues faster and more safely by keeping the rifle shouldered, observing the charging handle and manipulating the weapon based on what it tells him. The charging handle acts like a visual gauge for diagnosing the problem. Unfortunately, a lot of that information is lost when a more convenient but non-reciprocating charging handle design is used.