Consider another case that people who dismiss intuitions would have to dismiss: Saul Kripke’s Naming and Necessity. Naming and Necessity is seen as a classic in philosophy circles, so dismissing it outright is a pretty heft price. Here’s why they would have to dismiss it: Kripke’s arguments generally rely on intuition.
For instance, Kripke talks about what we would think if such and such were the case. Kripke obviously knows what he thinks about the situation, and he wants (and expects) us to think it too. However, this thinking we are supposed to do is really intuition.
More specifically, take his example of Feynman. Most people cannot give a description that uniquely identifies him (the position held by those he is arguing against). At most, they could say that he is a famous physicist, but that applies to other people too. However, those people are clearly referring to a person, namely, Feynman. But how do we know this last claim that they really are referring to a person and that person is Feynman? The answer is that we know it through intuition. Hence, to dismiss intuition is to dismiss Kripke.