The brains we have can be considered to have 3 different sections: the reptilian brain which is largely reactive and instinctual, the mammalian brain which works with emotions and memories, and the human brain that has higher thinking centers. Within the human brain is a powerful ability to model others minds, which in a sense is a form of telepathy, because we try to build models of those around us to understand them and see them. That isn't a rational process, it's subconscious and autonomous. It's paired with the broader function of our prefrontal cortex, which has the similarly amazing function of predicting the future, allowing us to predict and plan for future events.

To "fire on all cylinders" as a human with a big wrinkly brain then, you need to accept all modes of thinking. The rational brain is important because it can be used to reach places that are unintuitive through logic and reason, but the irrational brain or the subconscious brain is also equally or even more important because it can be used to places that are intuitively understandable but not necessarily rational or logical. That's why the paradox of understanding logically that the universe is meaningless, valueless, and senseless coexists with the understanding that there is nevertheless an intuitive meaning, value, and sense to the universe, and doesn't need to be rationalized. Both are true, but both are false. But depending on the situation, certain things are more true in that they are more useful to go with.

So while I agree in some ways, I'd suggest that you shouldn't make it an either/or situation.

If my view is correct, then your intuition does still need to be trained like your rational mind, and that's the benefit of society's ancient wisdom -- to help your intuition "kick in" and be able to use telepathy requires a base of intuitive knowledge about other people you don't automatically get, and that would be why some people are better "telepaths" than others.