The fundamental error that causes misuse of p-values (and statistics in general) is misunderstanding what statistics is in the first place. Statistics is applie

The fundamental error that causes misuse of p-values (and statistics in general) is misunderstanding what statistics is in the first place. Statistics is applied epistemology. There is no algorithm that fits all situations where you're trying to think about and learn new things. It's just hard and we have to deal with that. Arguably, the main point of p-values is trying to prevent people who really know better from "cheating" by reporting "interesting" results from very low sample sizes. Having a very rigid framework as a rejection criteria helps with this. However, the scientific community and system are not capable of dealing with "real cheating" that includes fabrication of data. Also, any such rigid metric is going to be gamed. Of course, there are some people who would also cheat themselves and maybe learning about p-values makes this less frequent. But such people using them don't understand what those values are telling them, beyond "yes, I can publish this". This is counterproductive because it prevents deep thinking and thorough investigation. Most scientists realize that in practice there is no simple list of objective criteria that tells you what experiments to perform and how exactly to interpret the results. This takes a lot of work, careful thinking, trying different things and very much benefits from collaboration. But who's got time for that? There's papers to publish and grant applications to write. So p-values it is. Or maybe some other thing eventually, that also won't solve the fundamental problem.