I think there's an issue in the question about the ambiguity in the term "effect" or "effect size".

To me, it makes sense to talk about effect size for an observational study.

If I observe the height differences of boys and girls in a school, it makes sense to report the difference in mean heights (an un-standardized effect size statistic) or Cohen's d for this difference (a standardized effect size statistic). There is no implication that we are intervening to change gender and that is causing the effect.

Likewise if I observe that ice cream sales are correlated to drownings in swimming pools, it makes sense to report the correlation coefficient, r, which is an effect size statistic. Again, there is no implication that eating ice cream causes people to drown.

I think people should be reporting effect size statistics.

Thanks Sal Mangiafico for your answer. This is very very helpful. BTW, my question is specifically about reporting the "effect sizes", not "effect" (sorry for the ambiguity).

May you kindly clarify the reasons that why many highly cited and high quality articles and theses don't report effect sizes. I am trying to research this topic but have not found any reliable answer or a resource that i could cite in my dissertation. Thanks in advance.

When I said "ambiguity", I didn't mean ambiguity in the question. I meant ambiguity in the language. Sometimes when we say "effect" we do mean in the sense of "cause and effect". And some people may bring this meaning over into the analysis of experiments.

I assume that authors often don't report effect sizes because traditionally --- at least in some fields --- we have emphasized hypothesis tests and p-values as the important results to report. In these fields we have done a poor job educating students about the importance of considering effect size and the practical implications of statistical results.