Third you need a person who has been tainted by the Ascian's teachings sufficiently enough to be able to actually summon the beast in the first place. Otherwise you won't be able to summon it to begin with.

Point is, a Summoner who never learned the Ascian's Ritual for summoning a Primal is not going to be able to do it, and the number of Crystals we have access to is not sufficient to even attract a Primals attention. Nor is there any reason why we would bother with Tempering countless individuals as we are heroes not villains.