The p-value cutoff of 0.05 just means "an effect this large, or larger, should happen by chance 1 time out of 20". So if 19 failed experiments don't publish and the 1 successful one does, all you've got are spurious results. But you have no way to know that, because you don't see the 19 failed experiments.
This is the unresolved methodological problem in empirical science that deal with weak effects.
More like "an effect this large, or larger, should happen by chance 1 time out of 20 in the hypothetical universe where we already know that the true size of the effect is zero".
Part of the problem of p-values is that most people can't even parse what it means (not saying it's your case). P-values are never a statement about probabilities in the real world, but always a statement about probabilities in a hypothetical world where we all effects are zero.
"Effect sizes", on the other hand, are more directly meaningful and more likely to be correctly interpreted by people on general, particularly if they have the relevant domain knowledge.
(Otherwise, I 100% agree with the rest of your comment.)
"Woman gives birth to fish" is interesting because it has a p-value of zero: under the null hypothesis ("no supernatural effects"), a woman can never give birth to a fish.
I suggest reading your comments before you post them.
My point was basically that the reputation / carrer / etc of the experimenter should be mostly independent of the study results. Otherwise you get bad incentives. Obviously we have limited ability to do this in practice, but at least we could fix the way journals decide what to publish.
The peaks in your spectra, the calculation results, or the microscopy image either support your findings or they don't, so P-values don't get as much milage. I can't remember the last time I saw a P-value in one of those papers.
This does create a problem similar to publishing null result P-values, however: if a reaction or method doesn't work out, journals don't want it because it's not exciting. So much money is likely being wasted independently duplicating failed reactions over and over because it just never gets published.