I think there used to be wording in older codes - like 1996 and/or before that did allow flexible cord in canneries, dairies and other similar applications. We still maintain them that way at a place I frequently do work for even though I don't see it specifically permitted anymore. My thoughts from experiences at such places is that things like motors that are washed down frequently seem to get less water in the terminal box if supplied with a cord/and water tight cord grip then a motor fed by liquidtight flexible conduits.
We also have situations where a pump is just out there in the middle of the floor so to speak and the only easy way to power it is a cord drop from the ceiling. You can't make a drop of flex from the ceiling without something to strap it to periodically (every 3 feet with 1/2 and 3/4 flex), and putting something there to strap it to just makes sanitary conditions harder to comply with. Cord works great even if it don't quite meet NEC. We have added watertight cord plugs and connectors to majority of them many years ago to have a place to disconnect for LOTO purposes, this maybe makes them a little more compliant as a cord pendant IDK. Passing the cord through walls or ceilings is definitely not NEC compliant, but as long as the pendant is completely exposed and routed from wall or ceiling enclosure to the supplied equipment located fairly directly below or immediately adjacent I don't have much issue with it in that kind of application.