There should be a Romex connector or strain relief bushing where it enters the disposal. It should not be directly on the edges of the entrance opening without being protected from abrasion damage.
I don’t see properly secured NM under a sink as subject to damage. It is the common installation method that I am familiar with. I have never seen a cord and plug connected disposal.
Connections between NM and the disposal leads would not be any different that connections to a lighting fixture.
You will not find a cord cap that is listed for use with NM cable.
You are likely going to see all kinds of homeowner installed crap as a home inspector. The frequency of times it is seen does not change it and make it right. Just as orange (or any color) extension cord is not appropriate wiring for use as permanent house wiring, Romex or any other NM cable should not be used for applications like garbage disposals, where an appliance (stranded / flexible) cord with an approved plug should be used.
I do see ALOT of cord connected disposals. The NEC allows this type of application with length limitations and properly listed cords. NM Cable would not be allowed for this applcation with a plug attached to the end.
Bob, In your pic I would certainly say it could have followed the cabinet surface better and could be neater and not being secured. I would have used a Panduit clamshell to secure it and kept it much neater.