In statistical thinking there is a tenancy towards conservatism

In statistical thinking there is a tenancy towards conservatism. The investigators, enthusiastic to obtain positive results, may prefer favorable conclusions and may tend to over-interpret the data. It is the statistician's role to add objectivity to the interpretation of the data and to advocate caution.

On the other hand, the investigators may say that conservatism and science are incompatible. If one is too cautious, if one is always protecting oneself against the worst-case scenario, then one will not be able to make bold new discoveries.

Which of the two approach do you prefer?

When you formulate your answer to this question it may be useful to recall cases in your past in which you where required to analyze data or you were exposed to other people's analysis. Could the analysis benefit or be harmed by either of the approaches?

For example, many scientific journal will tend to reject a research paper unless the main discoveries are statistically significant (p-value < 5%). Should one not publish also results that show a significance level of 10%?