Fieldmouse - sorry to disillusion you but I've spent my entire adult life using micrometers and calipers and performing inspections of many critical items sometimes to .00001" and 1mm or as you say, the thickness of a dime (actually slightly less) is a lot. This can easily be seen in verticle or horizontal alignment using a nocked arrow by the well trained eye. And I've been setting up compound bow ever since their existance. Also don't forget arrow spine. That also plays a critical role in arrow flight.
My bows can shoot bare shafts accurately out to at least 30 yards and can shoot groups better than I can hold at 70 yards.
I didn't argue your method. I just explained what I do and the tools I use.