I think most people don't care how many (hereinafter precision) Sides / Segments (hereinafter Sides) their Arcs, Curves, Circles, or Pies (hereinafter Arcs) have. They usually just want their Arcs to look smooth. I believe making precision relative instead of absolute, would eliminate 80% of the fiddling.
Currently precision defaults to arbitrary values. I think precision should be set automatically while drawing, based on the degrees of arc. The more degrees of arc, the more Sides will be needed to make it look smooth and vice versa.
Additionally, I think that the Measurements Toolbar, besides the Sides input box, should have a Precision input box or slider. This would set the Sides / Circle. For example, setting 360 would make a 90 degree Arc with 90 Sides while inputting a 180 would make a 60 degree Arc with 30 Sides.
Finally, I think that in addition to (or possibly instead of) the Tray's Smooth Edges Dialog, there should be an Arc Precision Dialog. This wouldn't just change the look of Arcs like Smoothing does but change the actual number of Sides of selected Arcs. There could also be a Global check box that would change the precision of all Arcs in the Model.