I have no doubt that loyalty to the Horde is one of Vol'jin's primary motivations. However, the shadow hunter has proven himself a master of the long game, and so we too should look up and down the playing field and see what Vol'jin might be thinking.
Old hatreds die hard
The first thing one has to consider when looking at the Zandalari plan is who they came to first. They dismissed the Sandfury of Zul'Farrak and obviously did not attempt to recruit the Drakkari of Zul'Drak (the Drakkari being legendary for their hostility to others, as well as mostly destroyed by the Scourge and their own god-eating ways), instead focusing their efforts on the two oldest and most powerful troll nations besides their own. The Amani and Gurubashi empires were the direct descendants of the ancient troll nation that died defeating the Aqir.
It made perfect sense to recruit these two troll nations. Both still control large swaths of land and have designs on larger territories that they once controlled (the Amani once held all of the Horde's territory in Lordaeron, effectively, while the Gurubashi controlled the entirety of Stranglethorn Vale). Tribes like the Smolderthorn or Frostmane would flock to the banner in time if it was supported by these two largest nations, especially since the Amani were the strongest group of Forest Trolls and the Gurubashi the strongest Jungle Troll tribe.
The problem with that plan is twofold from Vol'jin's eyes. First, yes, the Darkspears are loyal to the Horde. But also, the Darkspears hate the Gurubashi. It was the Gurubashi who harried them out of Stranglethorn entirely, forcing them to scrape an existence on remote islands. It was the Gurubashi who would hunt young Darkspears for sport. Well beyond there being no love lost between them, Vol'jin can easily blame the Gurubashi for the death of his father at the Sea Witch's talons.
Another reason, however, is pure pragmatism. The Zandalari may see the Gurubashi as the strongest of the jungle trolls, but Vol'jin commands the largest unified force of jungle trolls extant. Vol'jin's people haven't dabbled in Hakkar worship. While the Gurubashi were raided by Horde and Alliance explorers out to stop Hakkar, the Darkspears have reconquered their home base, recontacted the loa, brought themselves into a new relationship with them. Only the Darkspear, of all trolls, have druids. Why should Vol'jin meekly accept Gurubashi rule? What have they done in the past half decade to prove their fitness to rule aside from being nearly destroyed by their own foolishness and then signed over their people to the Zandalar?
The rise of the Darkspear
Vol'jin has displayed in the past year a keen, penetrating and restrained intelligence that tallies up the odds for any course of action quite effectively. He is, to a degree, a most un-trollish troll. Patience is not the strongest suit of the trollish people, but Vol'jin is displaying that he has mastered it more than most. (The fact that he threatened to kill Garrosh does show that there is a troll in there after all.) If we look at how exactly Vol'jin is pursuing his war plans against the Zandalari, we can see signs of that patience.
First off, his preparations against the Gurubashi were exceedingly well done. He managed to enlist Alliance forces without direct contact with their leadership, then brought together the hunters of the Nesingwary expedition, the local settlements, and even the goblins of Booty Bay under his control. In so doing, he set up a perfect front to oppose the Gurubashi without having to invest much time in it. These forces each have their own reasons for attacking Zul'Gurub, and that's fine by Vol'jin. Whether they be after treasure or their own personal safety, the important thing is that they've become a weapon in his hands.
Against the Amani, against whom he has no personal animus, Vol'jin actually acted more directly. He informed the local blood elves (and their high elf cousins, amazingly enough) of what the Amani were planning, then led a Darkspear strike force inside to liason with powerful Horde or Alliance special forces. His willingness to get his hands dirty in Zul'Aman seems likely to stem from his own understanding of the nature of Amani Warlord Daakara, who is in no way a Zul'jin. (As a player who raided ZA when it was relevant, hearing Daakara go on about how the Amani have the Zandalari as friends now was kind of nauseating. Zul'Jin didn't beg for help like a kicked dog.) Vol'jin's two-pronged attack on the Zandalari via these two allies gives one pause. What's the endgame?
On the strongest
By leading the attack against the Zandalari plan as he has, Vol'jin has proven several things.
The Darkspear are a force to be reckoned with in troll society. The Zandalar, the oldest surviving troll tribe descending back to the ancient troll empires, has been balked by an upstart tribe that once got kicked out of their own home. In his years of leadership of the Darkspear and his participation in the Horde, Vol'jin has learned how to keep the Darkspear whole and united, and he's just proved that they are exactly that. Rastakhan may claim kingship over all trolls, but he has to deal with Vol'jin now, if not as an equal, then definitely as a threat. This gives Vol'jin and the Darkspears enormous status among the disparate troll peoples. Right now, it is the Darkspear and not the Gurubashi who come out looking like the strongest jungle trolls. With the Revantusk firmly allied to the Horde, they may in time even come under Vol'jin's banner, and he'll have a force of both jungle and forest trolls to command.
Vol'jin has proved himself a leader among the Horde. By defeating the combined might of the Gurubashi, the Amani, and the Zandalari and doing do without the help of his nominal Warchief, Vol'jin has finally stepped out and displayed Darkspear might openly. The Echo Isles were a victory, yes, but they were a shadow victory at the tail end of a period of disappointment and tragedy. This victory is unvarnished, public, very clear, and was achieved through Vol'jin's guile, diplomacy and tactics. It not only shows off the Darkspear and their leader, it does so in a way that completely contrasts Garrosh's failures in Stonetalon (where he failed to control his own people), Ashenvale (where the Horde has bogged down) and the Southern Barrens.
Vol'jin can work well with others. In this operation, he enlisted and worked with Booty Bay, the Silver Covenant, even Alliance forces from Stormwind. He did so without making any concessions to them or in any way indebting himself to them, while presenting himself as a forthright and responsible leader who could be reasoned with and dealt with.
Vol'jin and the Darkspear come out of the war with the Zandalari in the strongest position they've ever been. They've proved themselves a capable, unconventional military force led by a tactician who counts the cost of every move he makes. Frankly, Vol'jin is now the most powerful troll on the face of Azeroth. The Horde may well prove too small for him, given time.
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