The definition of Attachment Plug (Plug Cap) (Plug) implies flexible cord is the only acceptable use, "A device that, by insertion in a receptable, establishes a connection between the conductors of the attached flexible cord and the conductors connected permanently".
If you go to 400.4, for Flexible Cords and Flexible Cables, "The use of Flexible cords and flexible cables other than those in Table 400.4 shall require permission by the authority having jurisdiction." Type MC cable is not listed in table 400.4 and since it has it's own section with uses permitted and not permitted, I would say it is not a flexible cord. The uses permitted for MC would conflict with uses permitted for flexible cord.
Now for receptacles, the mounting of them defined in 406.5, specifies "Receptacles shall be mounted in identified boxes or assemblies. The boxes or assemblies shall be securely fastened in place unless otherwise specified elsewhere in this code"". The handbook below this section points out, that "receptacles in pendant boxes are permitted if the box is supported from the flexible cord in accordance with 314.23(H)(1)."
And as previously mentioned, a flexible cord is not type MC cable.
If you compare the construction specifications of a flexible cord to that of a MC type cable.
For example, Flexible cords are required to be copper with flexible stranding. They have insulation thickness requirements. MC cable's construction is geared towards a wiring method for being securely installed rather than installed with strain relief outlets.