If we focus on medical research; performing a study involves taking a risk and potentially harming people. This is acceptable within bounds defined by the Principle of Equipoise as outlined in the Declaration of Helsinki. Prior to recruiting even a single subject to a study, the protocol must be reviewed and approved by an ethics board, usually an institutional review board (IRB). Many medical centers include a statistician or epidemiologist on such boards, and they consider the statistical feasibility of the study. That is to say, the protocol statistician has outlined the assumptions and the anticipated effects and applied the necessary formulas to provide rationale for the specified sample size(s). There are a number of questions to consider subsequently: are the assumptions reasonable? Is the analysis well powered? Does it make sense to recruit this many people without additional preliminary research? Will the potential benefits in the population after the study outweigh the risks in the study participants? And so on...
The constitution and mission of an IRB is outlined in the Belmont report. Just a plug, IRBs within medical institutions often have difficulty recruiting and retaining statisticians. If you are a biostatistician within an academic medical center, ask whether there is a seat for a biostatistician to participate.
The result of a successful medical trial is that standard practice can be updated based on what is known. Typically, this does fall down to a trial showing a significant result. One can hope based on the input of IRBs, and the natural limitation of cost, that the design feature under study has a reasonable profound impact on health so that the significance is compelling in its own right.
There is a flipside to this. Much less can be said of non-experimental, large EHR based studies which often show significant effects that can't and shouldn't be translated into practice. Open data sources and semi-closed data sources often do not have a steering committee to review the ethics of proposed research. Conversely, many languishing areas of healthcare continue to hem and haw over results due to the failure of trials to show unequivocal results, such as sodium reduction, cognitive behavioral therapy, fish oil supplementation, low fat diets, some vaccines, and so on.
In summary, for any confirmatory study, no there is no point to conducting a hypothesis test unless a power/sample size calculation has been performed - and the primary endpoint(s) is/are formally powered and secondary endpoints are reasonably powerful or important. In any other case, the analysis should be treated as exploratory, and a "hypothesis test" in this framework can be viewed as yet another method to identify research topics or detect effects - in that case, the statistician should be completely transparent in the reporting of their results.