Has belief in the supernatural succeeded in explaining anything?
Of course not.. anymore than the game of basketball. (Religion is a game of rules relating to obtaining salvation)
I think you're conflating two ideas, ie,
Human belief in or expereience of the supernatural
Belief and experience are two separate concepts.
Religion is testimony based, so by definition it is discounted by science.
That's where the problem lies.
You made a statement(maybe on another thread) that you would have to reconsider your stance on atheism if you experienced the 2nd coming.
To be self consistent you would commit yourself to be evaluated for schizophrenia.
So you accept testimony if it is your own.
Or maybe if it is your own and is shared by the rest of humanity.
What if one person were left out?
What if it were you in the loo?
What if it happens to you and a small group?
To yourself alone?
To a lifelong personal friend?
At some point you discount testimony.
In all the above the experience is the same. But in one (or more) you accept the experience and in the rest you reject it.
Reasonable and rational enough, but it really has no finality of proof that you are looking for.