Quote:
Y'mhitra: The Allagan Empire reached its peak during the Third Astral Era. Dissatisfied with dominion over Eorzea alone, this thriving civilization sought to expand its borders to ever more distant lands.
Y'mhitra: Eventually, the empire cast its avaricious gaze upon the southern continent of Meracydia. The peoples of these nations did not, however, take kindly to being invaded, and they summoned the primals to repel the Allagan forces.
Y'mhitra: Hard-pressed by these incarnations of elemental wrath, the leaders of the empire's military were forced to alter their tactics. They ordered the mages under their command to devise some manner of magic with which to counter the primals, and, after much experimentation, the art of summoning was born.
Y'mhitra: The magic invented by these arcane pioneers met with great success, and, within the Allagan Empire, the title of “summoner” earned the bearer an uncommon measure of awe and respect.
The quote above, to me, suggests once perfected that the art of Summoning was issued to highly skilled mages. It makes sense that they'd atleast infuse them with a weaker Primal's essence and it'll be up to them to master the Egi. We know that the Allagan Empire did not send flesh and blood soldiers, but instead relied on Robots and artificially created life-forms. It's alot more efficient to infuse their mages with a weak captured Primal.