Was Arthur a king or just a battle commander?

Explorations in Arthurian History

The figure of Arthur begins as a war hero, the praises of whom are sung in war poems by the Celts and the Welsh. Y Gododdin celebrates one particularly brave warrior, then says he "was no Arthur." The Triads are full of wonderful, courageous things Arthur did.
The most important early source for Arthur's deeds is Historia Brittonum, written by the monk Nennius in the 9th century. Nennius calls Arthur dux bellorum and tells us of 12 great battles Arthur fought. Although Nennius tells us the location of each battle, those locations are hard to come by these days. Scholars are still arguing over the locations. Even the agreed-on locations suggest that Arthur got around--literally--from Scotland to the lowlands of Wessex to Wales.
He fought everywhere. He won great victories. A strong tradition has him a Roman heldover who uses his knowledge of cavalry to rout the Saxons time and again, counting on their inexperience in fighting mounted men.
And even though the authors likely have exagerrated his deeds (killing 960 men single-handedly, for example), Arthur is likely to have been a bona fide war hero, a man who led his countrymen to victory time and again. It is certain that the Battle of Badon Hill, wherever and whenever it was, set the Saxon occupation back for a good many years. Whether Arthur fought at the battle is still not proved, but is generally believed.
Arthur was conceived amidst a war and was mortally wounded in a particularly bloody battle. His life was full of battle; it was the word of the times.
But was he a king in the traditional sense? The legends name him High King of Britain, a title held by his father, Uther Pendragon, and his uncle, Ambrosius Aurelianus. Noted historian Geoffrey Ashe identifies Arthur with Riothamus, who was called the King of the Britons even though he operated mostly in Gaul (Breton territory). A recent book by Graham Phillips and Martin Ke