The sharpening tool allows you to specify the specific b-factor you would like to sharpen the map to. This is helpful for comparing two maps, because maps sharpened by different b-factors can appear significantly different.
Yes, the b-factor is estimated, plotted, and applied at the end of the refinement. However, the estimated b-factor can vary when parameters change (e.g. non-uniform vs homogeneous refinement, marginalization enabled/disabled, etc.). So, the sharpening tool is provided as a way in which you can manually override these b-factors, and sharpen any map to the desired b-factor. When doing careful comparisons between two output maps of the same dataset with different parameters, I will pass them both through a sharpen job with the same b-factor, and download and compare these maps, rather than the ones output by refinement.