Ruling out physical, 'mechanistic' - in other words, knowable - explanations has a long but less than auspicious history. My own private name for the phenomenon is "Haldane's Error".
Once it was widely believed that lightning was a direct expression of divine fury - so much so that Benjamin Franklin's proposal of lightning rods was considered hubristic, even heretical. Meteors were felt to be obviously supernatural - what besides magical forces could have held a rock suspended in the sky? - until orbital mechanics were understood. Consider this quote from a prominent physician, J. S. Haldane, close to a century ago, discussing the "mechanistic theory of heredity":
On the mechanistic theory this [cell] nucleus must carry within its substance a mechanism which by reaction with the environment not only produces the millions of complex and delicately balanced mechanisms which constitute the adult organism, but provides for their orderly arrangement into tissues and organs, and for their orderly development in a certain perfectly specific manner.
The mind recoils from such a stupendous conception; but let us follow the argument further... This nuclear structure or mechanism must, according to the mechanistic theory, have been formed within a very short period by the union of two others - a male and a female one. How two such mechanisms could combine to form one is entirely unintelligible, and the observed details of the process tend only to make it, if possible, more unintelligible. When we trace each nuclear mechanism backwards we find ourselves obliged to admit that it has been formed by division from a pre-existing nuclear mechanism, and this from pre-existing nuclear mechanisms through millions of cell-generations. We are thus forced to the admission that the germ-plasm is not only a structure or mechanism of inconceivable complexity, but that this structure is capable of dividing itself to an absolutely indefinite extent and yet retaining its original structure...
There is no need to push the analysis further. The mechanistic theory of heredity is not merely unproven, it is impossible. It involves such absurdities that no intelligent person who has thoroughly realised its meaning and implications can continue to hold it.
Reading this passage, it's striking how clearly he recognized the functional requirements that a mechanism for inheritance would have to meet. But he could imagine no physical arrangement that could satisfy those conditions, and concluded that therefore such a mechanism was impossible. Indeed, he insisted that a spiritual explanation was the only remaining option. Laborious work by Watson and Crick (and Wilkins and Franklin) has since discovered DNA, however, greatly illuminating that which was previously obscure.
What if Dr. Haldane had decided to "push the analysis further"? Might we have discovered the structure of DNA decades earlier? (It's a historical irony that J.S. Haldane's son, J.B.S. Haldane, became a founder of the field of population genetics and was a key figure in the development of the neo-Darwinian synthesis.)
The wonderful essay by Neil deGrasse Tyson, The Perimeter Of Ignorance, presents many more examples of this phenomenon, most of them much earlier. But Dr. Haldane had such a grasp of what was needed, and so clearly and explicitly gave up, that he remains for me the exemplar of this trait.