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If you start studying everything that some eccentric rich uncle wants to give money to, you're going to get a high rate of false positives. If the True Probability of an event is very low compared to the noise in the experiment, the number of apparently significant results that are really due to noise will be much larger than the number of true positives. Of course, we do not know the true probability, but in some cases we have a pretty good idea.
While false positives are not a problem in principle, when you combine it with the well-known bias against publishing negative results and the fact that the metastudies needed to weed out false positives are time consuming (and then add the way pressure groups, newsies and outright frauds like to seize upon a single scientific paper, regardless of quality, to justify their cause, angle or story1), it actually does make sense to refuse to study something that can present no physically plausible mechanism of action.
Which is not to say that science doesn't have fads and that the scientific community isn't pretty conservative - sometimes excessively so. But obvious nonsense like homeopathy and wheels of perpetual motion really has no place in a serious research institution.
1That's not a problem for science per se, but most scientists do observe a minimum of social responsibility.
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