No, not at all. You have missed the mark completely here. This is totally culturally dependent. In a culture where this is expected, this is indeed what will happen. If you've only ever lived in such a culture then, yeah, you might get the mistaken idea this is an intrinsic human universal truth.

But cultural norms are really powerful and can absolutely overcome natural game theory / self interest dynamics. If everyone you know would think less of you after you quit a job when it is known that employers are loyal, you won't do it. Same goes for the reverse.