I don't know what Hintikka said about this. However, note that Hintikka argues against intuitions as an alleged source of evidence, which is their primary use in contemporary philosophy. As far as I can see, axioms aren't considered evidence. They are postulated. I think physicists are more careful in this regard because they explicitly speak about postulates, not axioms.

My take is that most texts in which intuitions are applied as a source of evidence (as opposed to an indicator for further inquiry) can safely remove any talk about intuitions and nothing of value and philosophical insight is lost.