It's possible the line workers would have never thought of this solution without having the inconvenience there to motivate them to. You could try to introduce a bonus to the worker who comes up with the most cost-effective and reliable idea though. It is probably very unlikely management staff would do that, since the engineering team has been "stretched thin" already and they didn't want to consult them.
I see people bringing up points like "What if the fan dies?" or "what if the weight of the boxes increases due to extra packaging?". IMHO, these arguments are invalid because of the same reason. Fan is not the solution.