I have lots of experience building CNC machines and designing hardware for CNC systems, the common practice is to use grounded, shielded, stranded wires. The bending radius is fairly large (> 30 cm), even on small machines, so cable fatigue is uncommon. In addition, hobbyist level usage is relatively low so even less incentive to go for really expensive cables. If I was building a machine that would run 24x7, I would go for them, though.
The number one problem (by a long shot) I see in one of the CNC groups I admin (130K members) - EMI from a lack of shielding and poor grounding. I think we hear around one bad cable report per year, if that. Spring for good quality connectors - that is the second most common reported problem.
On the point about plasma CNC machines. Yes, the EMI from cheap plasma cutters with "HF start" can cause problems. More expensive better quality ones use "blowback start" which isn't much of a problem. The solution - don't cheap out on your plasma cutter...