Thank you for posting the link to AC 91-70A noneya.
I was hoping to find a regulatory document requiring the use of a plotting chart to better make my point regarding the need to do so. Unfortunately I was unsuccessful in finding it and had to admit that I was at a loss to quote a regulatory requirement. As far as I am concerned personally, the company manual requirement is reason enough for me although I would still use the plotting chart even on an empty repositioning flight in a privately operated aircraft not on an operating certificate just because it makes sense to do so. The MNPS manual recommends the use of a plotting chart to supplement the master document (flight log) and that's good enough reason for me too until I know better.
In any case, obtaining MNPS approval from the FAA is aided significantly by following the "advise" contained within several ACs. On the operational side, pilots and operators benefit greatly by the fact that several highly regarded international procedures courses are offered which gather regulatory and procedural data from a great many different sources and present them as a single package to their clientele for what amounts to a reasonable fee when you consider the alternative.
My experience is strictly parts 91 and 135 bizjet ops so I don't know whether certain part 121 ops employ some alternative means in lieu of using a plotting chart. It just seems to me unlikely that they simply decided it's not necessary. Besides, what a nice thing it is to see your various contingency ETPs right there on the chart (as you plot your progress) along with what you are expected to do (side panel on the brand we used) in each of those contingency cases though. Thank you Cap'n Jeppy and other fine chart makers!