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The "battle" rifle defined so precisely, technically and eloquently in gun mags and wiki articles doesn't have that role anymore.

No, it doesn't have that role anymore, but it DID. And therefore is deserving of the name, and keeping it.

Saying anything else is akin to telling the veterans of the Indian Wars that the REAL battle rifle was the larger caliber 58 Springfield and not their 'reduced caliber' 45-70 trap door.

Or the WW-1 vet that his 30-caliber '03 Springfield wasn't a real battle rifle, the 45-70 was.

I don't see the logic in this statement, sorry.

Battle Rifle and Assault Rifle are defined classes, defined by their physical characteristics, not their use.

The 5.56/Stoner-design is -- in fact -- our current battle rifle.

Again, I disagree with your terminology. The M16/M4 series is our current SERVICE RIFLE. It is an Assault Rifle .

Designed for and effectively used it -- all practical ranges for all practical purposes for the common infantryman in deserts, fields, cities, barrooms ... every where for every thing.

The original intent of the designer, and the uses to which developments of their designs are put can be very different things. Stoner worked for a division of Fairchild Aircraft and the AR 15 was created as a technical exercise, a test bed to use aircraft alloys and "plastics" (fiberglass) and see how light they could make it, and how well things worked and held up. Early prototypes (not looking much like the M16) got the weight down to around 4lbs and were in .222 Rem. Further development led to a rifle we would more easily recognize as the AR 15 we know today.

It was not made to be, or initially marketed as an infantry rifle. When the Air Force lost Army support for their M1 carbines Gen LeMay needed a replacement. He was introduced to the AR and got interested in it as a carbine replacement for his security forces. This got other people looking at it, and led to further development, the 5.56mm cartridge, and ultimately the MacNamara defense dept. fiat that it would be the standard infantry rifle.

I always thought AR stood for Armalite

It does. It is part of the company's model designation, you find it as part of the name of their guns. AR-7 was a .22LR "survival rifle" the AR-10, AR-15, AR-180, and their little known AR-17 12 ga shotgun.

Its the first two letter of Armalite and it stands for the company name, nothing else.

You could argue that the term "assault rifle" is a misnomer since by the time it was issued the Germans were fighting steadily on the defensive and being pushed back.

I suggest you research the Battle of the Bulge, where the Sturmgewhr most certainly saw use in the assault role. There were other, lesser well known German assaults late in the war, Nordwind in the Alsace and the drive to lake Balaton in Hungary in 45...Don't know off the top of my head if the Sturmgewhr was involved in those or not, but its likely small numbers were. The fact that none of the late war German assaults were enduringly successful leads to the general idea there were none, but there were, and each of them was initially successful, though none were able to secure and hold their objectives.