Does null hypothesis or significance tests through frequentist statistics answer the requirements of the science in medicine and public health?

The amount of significance attached to statistics and more specifically to the role of the null hypothesis and significance testing in the proving or disproving of a relation in medicine and public health and as integral to conduct of research requires involvement of a deeper thinking. Does this research (statistics driven) serve the larger benefits of science we should be conducting and has not science survived, thrived, and helped human living adapt to the continued challenges of the nature over past many centuries on this planet without unduly worrying about the statistical significance defining the relationships our ancestors theorized on the basis of repeated observations over time or through plain trial and error.