I certainly don't think a lack of empirical proof means an absence of phenomena - Well, no, or else scientists would have no phenomena to explain 
The absence of scientific explanation is neither evidence that a phenomenon doesn't exist, nor that the explanation is supernatural/magical/religious/alien. It simply means nobody's satisfactorily evaluated it yet. I remember when 'upwards lightning' was deemed - by scientists - to be some kind of optical malfunction suffered by air crew (thousands of them!) while dream pedlars claimed all sorts of things about it, mostly to do with alien intervention. Now there is a proper physical explanation, and scientists these days aren't so quick to dismiss eye-witness reports.
People should be able to discuss their experiences without being constantly asked to prove what is by its nature unprovable, though of course shouldn't be surprised if people look for a rational explanation first. - The thing is, they get terribly upset when people do look for, and indeed offer, rational explanations based on known facts. In threads on here, those of us with a more pragmatic approach keep being told to shut up because our "belief system" deserves no more respect than theirs. Empirical fact is not a belief system! Those whose faiths demand that they ignore empirical facts, in favour of "beliefs", seem unable to grasp the difference between my approach and theirs.
Evidence can be experiential or philosophical and both are valid areas of discussion, but they do not meet current scientific criteria for evidence and that should be accepted. - Yes, it should! By way of personal illustration, I have PTSD and have experienced psychosis in the past. These conditions affect my perception. I'm forever seeing the shadowy thing flitting across my visual periphery: it's a symptom of hypervigilance and means I need to do some mindful breathing. In the past, I could read people's thoughts and see their auras. Now, I am a perceptive kind of person (due to the hypervigilance,) but my paranormal abilities were tricks of my mind. My perception was flawed, not the science which said I was claiming the impossible.
I think it's lovely to discuss these things in reference to the chiaroscuro of human experience, but not when people dismiss practical attempts to explain 'mysterious' phenomena. That's how gaslighting works! It makes me very uncomfortable that the majority of folk on this planet actively believe in their religions' doctrines, despite overwhelming hard evidence that they are untrue. What makes me even more uncomfortable is that they're so ready to re-frame science as a faith, purely so as to dismiss it as inferior to theirs.
This may have been a bit rambly, sorry. Am tired.