The half pane of glass is appropriate in warm parts of the world where you want the heat to be removed as quickly as possible. I suspect some hotel executive thought it looked cool in Miami, then made it the standard for the whole chain.

It's not even appropriate there. Ventilation should be determined by the fan, not the aperture.

Even in Miami, I don't want the entire bathroom floor flooded, and I want to be able to close the curtain/door and increase the humidity in the shower.