Intuition has indeed played a role in the development of philosophy. It inspired Plato’s Ideas, and Aristotles concepts of impetus and forms.
But these ideas were mistaken. The idea of impetus, for example, was shown to be false by Galileo and Newton, and replaced by the concept of inertia.
Intuitions are heuristics, shortcuts. Some are innate, a product of natural selection. Some are acquired by experience.
But this means our intuitions are only “satisficing,” as biologists say, and only wrt the data they’ve been trained on.
Your last sentence presents a false dichotomy, one I’ve addressed in a previous post.
https://medium.com/original-philosophy/truth-as-process-b3347e56137c