Currently the whole plot is building up to our Free Companies actually being able to summon Primals fully.
True, it's just from a FF series perspective, it makes more sense for the Summoner job to summon them then just random people.

And even then they could have made the plot work. If a a summoner summoned a de-powered one, then an FC would be more people = stronger Primal.

But meh, all that is "What If?" arguments since it's really hard for them to rewrite what's already in the game.