Just finished the lvl 50 BLM quests.
Basically as a BLM you are indeed tasked with sealing the void. I won't say why to avoid spoiler territory (as much as I can anyway) just in case of whoever ends up reading this, but for the most part BLMs don't get their powers from the void. It's very much drawn from Aether both within and outside of the body. The entire storyline with the youngest brother centers on this as the main plot point: he doesn't have enough aetheric energy within himself to be a BLM. But BLMs can use potions and other techniques to draw power from the world's Aether (if I understood correctly). But yes: they do love making everything go BOOM!
So in that sense, a Void Mage could actually work. The void is all about sending terrible demon-like foes into Eorzea to feast on everyone's aether. So I imagine summoning specific voidsent would be one of the aspects of the job, though whether they'd be permanent like SMN's egis or more temporary attack animations would be a hard choice to make. But I could see them inflicting several debuffs and have mana drain/hp drain abilities as they "feast" on enemy aether.
