A piece of Romex, sailing through the air, just doesn't seem right to me- even when proper connectors are used.
Many times, there is no box at all - just a piece of wire coming thrugh a hole in the wall.

IMO, some kind of metal flex would be better.

I really think that anything that will need replacement ought to have some means at the appliance to disconnect. If nothing else, it reduces the temptation to work hot, and is much more convenient when troubleshooting.

I like cords & plugs, simply because there is less opportunity for the plumber, the HVAC guy, whoever to touch the electrical system. I really don't want them to begin to think they're electricians, too!