Whilst I was showering this morning I got into an idle thought mode and thinking strange things, as you do when doing mundane tasks..
I got to thinking how you’d make an accurate protractor using nothing other than a straight edge, a compass (not the north pointing kind) and a sharp pencil.
I determined that you could do it as long as you didn’t mark the divisions in degrees as below 45 degrees all the divisions would be fractional if you used the simple technique of sub-dividing an angle. (ie. from the origin make a chord which passes through lines from the origin subtending the angle, then find the point equidistant from each of the points of intersection between the lines and the cords and draw a line from the origin through the equidistant point.)
Surely, therefore, it would be better to have the circle divided into degrees which were based upon a power of two? In that way the whole set of marks on a protractor etc. could be generated by simple angle subdivision. Far easier and far more logical.
Of course, we can blame the current (non-radian) division of a circle on the Babylonians.. they have a lot to answer for do those Babylonians.