Proper frequentist procedure says that we should establish a sampling plan, statistical analysis and significance level before we start an experiment. We then report whether or not we reject H0 for the chosen level of significance.
What if we do the same and don't choose the significance level beforehand. We simply look for the lowest significance level we can get away with, and report that, stating that we can reject the null hypothesis with the given level as significance. The lower this value is, the more weight we can give to our analysis.
If we are upfront about following this procedure, is this honest? If not, where is the problem? I'm having trouble figuring out what the issue is, and why people don't report like this in general.