Around here NM and MC for that matter, is subject to damage <8'AFF. In fact we do alot of corrections on exactly that type of work. It's obvious of the hazard when you walk in to do the work, and find all kinds of things hanging on it. Like crowbars, boxes stuffed into the stud-bays, and once, a kayack tied to it. Even above 8', we pipe it unless it is planned to be rocked.
As far as Code goes, "protected from physical damage where necessary", is pretty subjective, and lends alot to the AHJ.
As for the boxes, as you mention,
314.17 (C) Nonmetallic Boxes and Conduit Bodies.
Nonmetallic boxes and conduit bodies shall be suitable for the lowest temperature-rated conductor entering the box. Where nonmetallic boxes and conduit bodies are used with open wiring or concealed knob-and-tube wiring, the conductors shall enter the box through individual holes. Where flexible tubing is used to enclose the conductors, the tubing shall extend from the last insulating support to not less than 6 mm (1/4 in.) inside the box and beyond any cable clamp. Where nonmetallic-sheathed cable or multiconductor Type UF cable is used, the sheath shall extend not less than 6 mm (1/4 in.) inside the box and beyond any cable clamp. In all instances, all permitted wiring methods shall be secured to the boxes.
Sounds like the boxes need clamps for NM....