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.
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.