Considering the fact that it takes all eight masks to reveal Konahrik, along with the meaning of the word itself (Warlord), it makes more sense that Konahrik was a position filled by a powerful dragon priest in times of war, similar to the Hortator in Dunmeri culture. The eight highest ranking dragon priests likely convened a council in order to decide who would take up the mask and the title, and the Konahrik mask was locked away so that no one dragon priest could acquire it without the consent of the others. Thus it makes sense that Vahlok possessed Konahrik, as he was the single champion chosen to personally defeat Miraak; considering its role as a temporary position, it would have been returned to Bromjunaar after Miraak was defeated.
Honestly, a bigger question is why there are four masked dragon priests on Solstheim (including Miraak). They do not have places at Bromjunaar, meaning that they did not have a place in the Dragon Cult's leadership, but they have masks, which were only given to the highest ranking priests by the dragons. And three of them, Ahzidal, Miraak, and Zahkriisos, also have two-word names; dragon priests who were given draconic names consisted of only one word.