On a number of occasions I've broken small plastic parts that are nearly impossible to replace but could easily be 3-D printed. The latest such mishap is the volume knob on the factory-installed radio on my car.
I have little experience in 3D printing, and would like to be able to replace these parts with something very close to the original. Spending hours measuring and designing a replacement part that should be $5 isn't really an option. I need something to scan the broken pieces in 3D and somehow just seal up the seam where it's broken.
Is there a scanning/printing/software system to do this that doesn't require a lot of 3D design experience?
The easiest way is as you currently do: model the pieces by hand, using (digital) calipers to measure them.
Scanning technology isn't very good, and the models are not of printable quality. Usually, fixing a scan is more work than modeling an item from scratch.