I only just finished 5.0, but I remember somewhere in the lead up or during Amaurot it's pretty directly explained that the Ascians are the source of the techniques to summon primals, but we fractured beings don't possess the aether to properly fuel them which is why they feed off the land instead.
Unless this is something I haven't gotten to in ShB yet, every Beast tribe has a group that hasn't allied with the Alliance that is responsible for continued primal summoning. Ardbert and the warriors from the First killed several primals during their time here before you came into conflict with them in Heavensward.