[kuhewa]

Nothing is wrong with publishing small effect size results. Setting a P threshold lower or a a higher bar for effect sizes for journal acceptance will just increase the positivity bias and also encourage more dodgy practices. Null results are important.

Understanding effect size is as important as significance can manifest by requiring effect size or variance explained to be reported every time the result of a statistical test is presented, e.g. rather than simply "a significant increase was observed (p = 0.01)" and also making that kind of parsing the standard in scientific journalism.