As Adam noted, direct CNC machining of plastic is not so common because it is, by nature, wasteful.
CNC machining is HEAVILY used in the manufacture of plastic parts, just not in the 'direct' line. CNC is used to make dies for injection molding, vacuum forming, extruding, and many other processes which are not subtractive, hence, there is no waste to gather up and either discard, or try to recycle.
Once the dies are made, parts can be molded at a much higher rate, and with much more repeatable quality, at a substantially lower cost, than fixturing it for subtractive machining process.
So in light of the manufacture of plastic products, applying subtractive machining process is basically a 'rework' circumstance... a second operation that should be corrected not as afterthought, but by fixing what went wrong in the prior steps to yield a part that didn't come out right in the first place.
5 Why. Kaizen. Six Sigma. Pull the thread... peel the onion... find out where the TRUE problem originated, and FIX IT THERE.
Woodworking... large-scale CNC controls are focused on common production... like setting up a sawing system for dimensioned lumber, or process control for making trim. The advantage it offers, is high-speed change of dimension, and quality control monitoring... it verifies dimensions, and records them, to look for deviations that suggest problems either with material, or machinery.