Research has been done in some cases; always, it either came up empty or there was some non-supernatural reason for the observed events.
e.g.:
blogs.scientificamerican.com/news-blog/us-and-soviet-spooks-studied-parano-2008-10-29/
Remeber, these were organizations ready to pour billions into having a small edge over the adversary and organizations knowing a few decades earlier when scientist showed up with a crazy idea cities were levelled and every dollar spent was at least to the standards of the organizations an awesome investment; so they would have grabbed at any straw to have a supernatural advantage; but they came up empty in the end, both sides, independently of each other.
One cannot conduct resarch to disprove some reported event. All one can do is to test whether under similar conditions the event happens again; no reported supernatural event ever passed that test and could be reliably repeated.
Hence, the conclusion that at least much what is reported is bogus. Making the search for the “real” thing like finding a needle in a haystack with the added caveat that the haystack might not contain any needle at all.
One cannot call offering 1 Million not an effort:
en.wikipedia.org/wiki/One_Million_Dollar_Paranormal_Challenge
I think the conclusion that no or nearly no realiably repeatable supernatural effects with statistically significant effects on the physical world exist at this moment in time, to be valid.
But the error is to conclude from this, that no supernatural effects exist, because the exclusion of non-reliably repeatable supernatural effects with statistically significant effects on the physical world does not exclude a host of supernatural effects; e.g. it doesn’t exclude that prayers are heard and answered, cause
usccb.org/bible/matthew/4
“Jesus answered him, “Again it is written, ‘You shall not put the Lord, your God, to the test.’””,
which i interpret to also include “and do not put the Lord, your God, to the test, especially all those scientific test happening beginning in about 1700 years; especially no mountain moving just for show or writing a paper, cause it is both sinful and won’t work as God is no lab rat and will ignore labyrinth and cheese you want to force Him to submit to.” (hopefully, my interpretation is not too far off).
Especially, any intelligent supernatural entity interacting with this world could always avoid having scientist find scientific evidence for its existence; it just would have to be more clever than the scientists; which is not only true for God, but also Angels both Non-Fallen and Fallen.