If you make the hypothesis first, 3-sigma is quite enough. Many physics experiments do exactly that, but famous high-energy ones don't.
(That said, not having an hypothesis beforehand was very common in psychology before the 21st century.)
Proving a known hypothesis or deciding what you want to know after the fact are completely different methods.
> Did you cast some ancient spell when you came up with the hypothesis or something?
"I'll know it when I see it" is an incredibly vague way of doing science that requires extra rigor somewhere else to compensate.
Or, in a more rigorous explanation, testing for multiple hypothesis is subject to that kind of failure:
So you need more data confirming your theory.
But if you state your single hypothesis beforehand, you are at the situation of the top square, with a high-confidence result.
In the face of all these potential confounders, more statistics and controls seem necessary than, say, in a physics collider experiment on electrons (each electron possessing exactly two characteristics, location and spin, and all such electrons behaving identically regardless of location or time). Yet, even in this setting of simplicity and reproducibility, physicists have still found it necessary to establish a stringent, five-sigma threshold for discovery — 3 sigma anomalies come and go. Such a stringent threshold is unthinkable in psychology due to practical considerations. Ergo, it’s hard for to see how psychology can become a reliable empirical science.