There's evidence for and against what you have to say, both in the Stormblood Primals. Susano-o didn't seem particularly interested in tempering the Kojin, but then again... his summoning wasn't exactly traditional. Kojin treasures are particularly prone to spawning primals when exposed to high aetherial levels though. They haven't made any known attempts to temper, in support of your baking argument.
However... Then we look at Lakshmi, another primal that was NOT summoned on purpose. She was summoned out of grief, and like the Kojin, the Ananta were never taught about summoning. Lakshmi appeared when the queen's daughter was killed and resurrected her. However, Lakshmi has been demonstrated to be the most temper-happy of all primals. The Ananta were pretty shocked when she appeared. They had no clue about anything relating to summoning.
I would argue it's just part of the natural skill set of a primal, as part of their self-preservation. It just seems to depend on the personality of the Primal as to how much they feel a need to do it, with Primals like Alexander deeming themselves to be too dangerous to the natural state of the world to allow themselves to continue to exist, thus Alexander didn't temper ANYTHING.