Ability to change starting point for closed path
Currently the only option is to cut and the path or redraw the path completely if the starting anchor is in the wrong place. For straight edges, such as a square or even a rectangle it's easy to work around, but when it's a curved edge it is difficult to replicate the same curve with the cut method. Could easily add this feature to stoke effect so that the starting point can be adjusted with a click on the anchor. Or have left and right arrows to move it to a different starting anchor (although that wouldn't work on things with many anchors it would assist with anchor points close together).
Good for brush strokes, svg, and other applications using the pen tool.
A workaround would be to cut a path in a point you want to be a starting one and then joining it back.
Not a fastest way, I agree, a command needed.
If you need a faster way — PathScribe plugin by AstuteGraphics has way to force a point to be a starting one in two clicks.
1000%! There is no artistry in applying a variable width profile that you can't control. You can edit the starting point on a path of text, why not brush and width profiles? Please Adobe, Please Please Please make it happen.