I agree, the wire should not be in the duct, that being the case, it is still protected more in the flex conduit than simply running armored cable (I think that is the name of it) up to the fan, something I see almost daily. It is under most older Mcdonalds fans, That is just not made to be moved like is required to take the fan on and off, and inevitably the armor starts to split open.
I did see armored cable running down the duct into the hood through the plenum and out through a hole in the hood where it was simply plugged into an outlet, they just unplugged it at night to turn the fan off. I was there to bid the job and tried to get a picture but the guy didn’t like me carrying a camera around his kitchen, after a quick survey I told him I couldn’t help him and left.