Why not power a motor from Arduino?

Thank you (and @jim-p) for pointing out my calculation error. I had inadvertently used the resistivity value in Ω·cm rather than Ω·m, which increased my result by two orders of magnitude. Here is my corrected calculation, which yields a result similar to yours:

Trace thickness (assuming 1-oz): 3.5×10-5 m
Trace width (from PCB CAD): 5×10-4 m

→  A = (3.5×10-5 m)×(5×10-4 m) = 1.75×10-8 m2

Copper resistivity: ρ=1.7×10-8 Ω·m

→  Resistance per length:
ρ/A = (1.7×10-8 Ω·m)/(1.75×10-8 m2) = 0.97 Ω/m ≈ 0.01 Ω/cm

Good point, but with the corrected resistance value, the voltage drop is no more than 100 mV even at stall.

So voltage drop in the PCB traces seems to be a non-issue for this case (i.e., this would not be a valid rationale for justifying why this small DC motor should not be powered from the Arduino 5V pin — I'm sure there are other relevant rationales, which remain to be clearly elucidated in this thread).