I actually did use Eidolons for the first half of the game.
In fact, Odin make Cid Raines, a supposedly tough boss, a walk in the park.
In addition to that, the boss at the top of Taijin's tower is also easily defeated with Odin.
And adamantoises can be defeated very early in the game with the help of summons and Vanille's death spam...​