No, grappling is perfectly fine for the military. Fighting over weapons is a grappling game more than a striking. (if we want to break it down into those two) If you want to disable somone weapon you either have to destroy the weapon, the hand that has the weapon or close in and grapple. If we also account for armour in the military, striking can easily equate to breaking your hands or knees on somone helemt or plate etc.
I belive history also backs me up on this one, grappling is the primary method for fighting in weapon systems, for the above reasons. (obviously striking exists, but its predominately about grappling the person, thats the folly with dividing it up into grappling and striking, you do both usually when doing either)
You also would ditch your pack in any actual fighting, especially if its a proper bergen, its too encumbersome to properly fire and move in for any signficant peroid of time (or at all), you would especially ditch it if you are room clearing or trench clearing or in any situation where you would engage in hand to hand with somone. Assualt packs can vary, but they are vastly less encumbersome than bergens, and are carried for as the name implies, assualting somewhere. (effectively where you dont need to lug around more than say 24 hours worth of equipment and food etc)
Uniforms are lighter today (at least for modern militaries) than they have been with full wool issue also and are pretty much neglible for the most part. Wool did have the issue fo it took on water, but thats only a safety issue for amphibious things. Plenty of people drowned that way or at least the wool didnt help in the invasion of normandy for example. (i dont think not wearing wool would have saved you if you couldnt swim and jumped off not remotely close to the beach)