The military uses ball powders because they burn slightly *cooler and the ease of loading by volume.
*Depending on deterrent coatings (burn rate) and nitroglycerin content.
"Much has been made about ball powders being cooler burning than extruded powders, but the fact of the matter is that there really isn't much difference. Flame temperature is very close to the same for all smokeless powders and runs about 3300 degrees F. Ball type powders tend to be from 3200 to 3300 degrees F and extruded powders tend to run 3300 to 3400 degrees F but there is wide variation."
A (Very) Short Course in Internal Ballistics
http://www.frfrogspad.com/intballi.htm
British Cordite powder was very hot burning and was not to be used in machine guns due to barrel wear. Cordite powder contained more nitroglycerin than many of todays double base pistol powders and "DID" wear barrels out much quicker. Todays double base rifle powders contain very small percentages of nitroglycerin and the deterrent coatings and additives make single and double base powders very close in peak flame temperatures. I use a lot of double base H335 and W748 in my AR15 rifles without complaint.
Below Cordite powder.
Catshooter
The M16 used the same ball powder used in the M14 rifle when it was first introduced a variation of Winchester 748. "BUT" the calcium used in this powder built up in the gas system of the M16 and caused just "ONE" of the jamming problems.
The main problem with the M16 rifle was the Army did not want to closed down Springfield Armory and turn over production of military rifles to civilian contractors. The Army did every thing possible to sabotage the production of the M16 rifle by Colt firearms. The Army sent 100,000 M16 rifles to Viet Nam for testing "WITHOUT" any cleaning equipment.

The Army kept changing the rifles specifications, two other firearms manufactures back out of their military production contacts and Colt almost went bankrupt. In the end it took Congressional investigations and intervention to straighten the mess out.
It is still a mouse gun and lacks punch and you should read more history about this rifle, I went in the service in 1969 and every M16 rifle I shot jammed and left a bad taste in my mouth about the military and contracting out.
It took me 40 years after I got out of the military and prodding by my two sons to "get modern" and buy my AR15 rifles. I'm still conflicted, every time I pull the trigger these rifles throw perfectly good brass away and make me go look for it. (and its still a mouse gun)
Some things never change.