I agree that spiritual experiences are likely a 'super intuition' that performs an integrative function.
I think it's important to distinguish between mysticism as a mode of perception that's part of our evolved human capacity and mysticism as the grounding to the type of claims that religions tend to make.
One highly evolved system aiming at mystical insight (3000 years of tradition in India) says that the core insight = Being, Bliss, and Awareness are One and that a variety of Yogas can get you to a state where that is obviously and numinously true...without this necessitating any particular divinity. (Granted this developed in a context in which gods were assumed...but the general trend was away from gods as actual entities and more toward them as the faces of the indescribable 'absolute'.)
It worth noting that a standard 'take-away' from mystical experience is it's ineffability. Yet your view of the world is changed.
My 2 cents: if ecstatic experience is part of our birthright, there's plenty of room for agnostic mystics.