Not publishing results with p >= 0.05 is the reason p-values aren't that useful. This is how you get the replication crisis in psychology.
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.
> "an effect this large, or larger, should happen by chance 1 time out of 20"
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.)
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.