Let's clear up a few things.

The Empire is indirectly responsible for all the primal summons in the Sixth and Seventh Astral Eras; prior to the attack on Silvertear, there were no documented instances of primal summons anywhere during the Sixth Astral Era. It is not directly responsible for all primal summons, but its activities do agitate people into summons, and its machinations have directly lead to at least one summon (Tsukuyomi).

Anyone with a lick of reason can't be swayed to the Empire's cause via reason and logic because the Empire's logic is circular. "We conquer other countries because they summon eikons, which they summon because we try to conquer them." Even Gaius figured it out - he wouldn't march on Eorzea again after the Calamity until he had a way to permanently deal with the primals, as he was aware the locals would summon in response to such aggression. (Lahabrea was only too happy to provide him with what he sought, and the rest is history.)

Let's try not to make this another Garlemald debate... please?