As with dishwashers, water heaters, circulating pumps, and several other household 'appliances,' we're getting into 'design.'
Some folks want to get all persnickity and say "but the code says ..." and split / parse / dissect every word as though it were handed down from Heaven and infallible. What seems to be ignored is the idea that, just maybe, the code, or this anal application of it, is plain wrong. I doubt language is capable of ever being 'precise' enough.
Please don't bring up the idea of 'precedent.' You might as well argue that all ships are required to hit icebergs, because we 'let' the Titanic do it onece.
Another comparison: speed limits. Is doing 50 in a 30mph zone a violation? What if you're doing 31? How about 30.00001mph? Does it really matter that you can't read the spedometer that fine? I don't see where the law required you to even have a speedometer. The law only requires you to obey the limit; how you comply is your problem.
That, my friends, is called the 'reduction to the absurd' argument. Carry anything to its' logical extreme and it's absurd.
So, as for all this worry about putting cords & plugs on equipment ... I'm not going to lose any sleep. Proper strain relief, proper size wire, proper plug ... I don't have a problem. I sure prefer it to a whip of Romex poking through a jagged hole in the wall, then entering unprotected and unsecured into a KO. I prefer finding a plug to finding an open junction box with wires dangling everywhere.
Having received a 9-hour power outage as a Christmas present this season, I am rather partial to the idea of mounting a second receptacle in the furnace cabinet, and having this receptacle ultimately connect to a small portable generator. Kind of makes the transfer both simple and goof-proof. I am partial to having heat on 25-degree winter days.
Flexible cords not approved for this use? Well, I'm not sure Romex is approved ffor the use either. I'm not comfortable with Romex sailing through the air for any distance - be to feed the furnace or the garbage disposal. For that matter, slipping a sleeve of flex over the Romex accomplishes .... what, exactly?
I'm not comfortable with forcing the serviceman to take apart wires to disconnect things. Why have him work "hot" when we can have him plug things in?