I think this particular quote is important. To be transparent, I added this to the wiki and not @ADAlthousePhD as indicated.
Regarding power, I think the paper by Moore explains it better than I can:
Schoenfeld suggested that preliminary hypothesis testing for efficacy could be conducted with a high type I error rate (false positive rate up to 0.25) and that subsequent testing would provide a control over the chances of a false discovery in spite of the initial elevated error rate. He suggested that this approach could ensure that the aims of the pilot study are completed in a timely manner due to the use of a smaller sample size. If such an approach is taken, it is important to remember that a pilot study should not be designed to provide definitive evidence for a treatment effect. It should, on the contrary, be designed to inform the design of a larger more comprehensive study and to provide guidance as to whether the larger study should be conducted.
My take-away from this is 1) place lower confidence in our results and 2) a pilot study should not be designed to provide definitive evidence. The gist of it being that they are underpowered to provide definitive evidence and should not be taken as such.
Anyway, I think the last point you make about bias is important, but I tend to think that bias and precision are related and both argue against doing inferential hypothesis testing in a pilot study. One of the purposes in my view of doing pilot studies in the first place is to try and identify sources of bias or challenges (for example in the screening/recruitment/enrollment/selection process of participants) which can affect estimates and their confidence intervals. 2-3 outlying observations can be wildly influential in this situation, and lead to a p-value < or > 0.05 and consequently bias future decisions w/regards to future trials.
My (relatively limited) experience with this is that although I would have liked to present data on outcomes descriptively, journal editors rarely if ever accept this and require some form of outcome-based testing regardless of the CONSORT extension for pilot studies. My pragmatic way of approaching this is to do some tests, report p-values and CIs and then making it abundantly clear that we will not be making decisions for a future trial based on these tests alone but interpret them with care and in light of the literature in general.