I fear that you are playing into the Bigfooter myth here that academia is not even allowed to explore the possibility of Bigfoot. Personally, I don't see the concept of a limit in this regard if a scientist wishes to look. Quantum theory arose because people were willing to re-examine what was believed to be very firmly established ideas in science. And these prior ideas were not wrong per se, but there was more to reality than had been previously known. So I do not like the general idea of "Well we already know that so we should stop looking."
I am well aware here of the truth in the old saying that "They laughed at Einstein but they also laughed at the 3 Stooges" (indeed they never laughed at Einstein). I am trying to be very clear that I am not reiterating the stupidity of "Well we don't know everything yet". It is very clear to me that there are no Bigfeet based on the existing evidence. Some concepts are so improbable, idiotic and convincingly proven wrong by science that anyone of any intelligence would not bother to spend time or effort re-examining them. I include here the existence of Bigfoot- I would place an investigation of the existence of Bigfoot approximately 145,258,290.891-th in my hierarchy of questions worth looking into. Because of the enormous weight of the evidence that Bigfoot does not exist. I would not look for Bigfoot or pay a nickel to have someone else do so. But I inherently do not think that scientists should be in some way prohibited from asking any question that comes to them. They can look for unicorns if they wish as far as I am concerned. If on their own "dime" and their own effort. Perhaps ideally they should be doing something useful instead- but in academia one is typically paid to teach whereas one's research topic is unpaid "spare" time (ignoring grants, which I already stated I would not favor for Bigfoot investigators).
Now in academia people are rewarded for revealing and proving some unknown fact. Is a Bigfoot investigator going to find Bigfoot? Not in my view. not ever. Should the continuing lack of finding Bigfoot lead to a devaluing of the researcher's abilities and judgement? Of course. But I would not bar them in advance from taking the gamble, even though I view Russian Roulette with an automatic as representing much, much better odds in terms of survival/success.
This is not saying that it is okay for the anti-vax creeps to spread their lies: it is just saying that academics should be free to continue to investigate, in better and better ways, if vaccines are safe (sometimes a particular vaccine does have a problem). I don't think that Bigfooters are correct to spread their nonsense or establish a department of Bigfootery- but if they want to continue to explore if Bigfoot is real, again on their own dime, I feel okay with that. Ideally the more negative results that they obtain will help convince some people of the truth that Bigfoot doesn't exist, but of course I don't think that will be the case for the most committed Bigfooters.
To be very extreme- I see the odds of a perpetual motion machine being zero based on known physics. Anyone seeking to invent one I would view as crazy or ignorant. But if, on their own time, they had an idea for how to build one, I would want them to test it scientifically.