Well, let's see ....

UL lists the cord.

UL lists the plugs for placing on the cords.

Put them together, as intended.... sure, the assembly is not UL listed - but that's a distinction without a difference. UL certainly has no problem with connecting the cord to the cable. That is exactly the circumstance for which the plug was evaluated. There is absolutely no code, or listing, issue with your assembling something, using materials as intended, in a manner that simulates a manufactured product.

To try to twist words and say otherwise would lead us to conclude that the plugs can never be used, for anything, because the specific 'assembly' is not listed. That's an insane extension of "logic."

There might be a problem with a home-made cord .... but to find that, one needs to dig deeper than surface appearances.

As for cords in place of permanent wiring .... cords are accepted where movement is an issue. Either movement for cleaning and servicing .... or due to vibration .... qualify.

Then there is the issue of passing the cord through a 'wall or partition.' I have no worries about a dishwasher cord passing through a suitably bushed hole in the cabinet side, a hole large enough for the plug to pass through.
Why? primarily because the code appears to both require a short cord, as well as require the disconnecting means to be accessible. I defy anyone to comply with both requirements when a dishwasher is mounted in a cabinet, under a counter. Either the cord has to be long enough to allow you to pull the unit out far enough that you can reach into the cavity ... or the cord has to pass through the cabinetry into a section you can access.
I would say that we have competing code principles here ...and, IMO, the overriding principle is that you be able to disconnect the appliance. IMO, any code requirements as to "how" are far less important than the "what" and the "why."

That's why the NEC starts off by stating the AHJ can deviate from the text, as he sees fit.