So, am I the only one who see's this..?

[Nonsensicles]

Not at all.

If the Primals share their power, and if by defeating one-after-another they can become stronger, then it's just as likely that one of the primals has declared war on the others.

Plus, chances could just as easily make it out that the "hatred of primals" was propaganda itself to conquer Eorzea. Just like how wars happen to gain support in the real world.

Also, if Primals can't actually die, just be banished, then a Primal who wants Hydaelyn all to himself would need to have those capable of summoning his rivals exterminated to their last, even those who wouldn't summon their Primal no matter what. Just in case.