It's likely because it makes it easier to see the consistency of the paint and how much is left, and makes working with the airbrush a little quicker: not only because you don't have to fiddle with the lid, and you also won't have to clean it.
In some cases or situations it can improve the flow of the paint when the hole in the lid has insufficient airflow (or is simply clogged) and temporary vacuums occur.
I doubt it is because it looks more interesting in videos, although allowing the viewer to see the colour under different lighting conditions could definitely play a role.
Reasons to keep the lid on include preventing spills and maybe keeping your paint clean when working in a dusty environment.
I have also read about users keeping them on so they can tilt their brushes every now and then to improve the flow of the paint.