The main purpose of having a gap is to prevent jamming the gears together. This happens because the gear teeth aren't a constant pitch radius relative to the bore of the gear, the gear shaft isn't straight, the inside race of a ball or roller bearing is not in line with the axis, or the teeth of the gear are made incorrectly.

Mostly these errors should require only 0.010 inches total of extra spacing, but it depends on the gears and bearings. On larger gears with oil lubrication, it is useful to not trap the oil at the bottom of the teeth, causing pressure and heat buildup as the oil is compressed and ejected. In watch gears extra gap is to prevent tiny particles from getting trapped and jamming the gear train.

In many gears, the clearance is cut into the gear by making the teeth narrower, so the optimum distance is the sum of the pitch radii.