Media Player, for audio you have consistent reasonings and you are encouraged to post your ideas to the Brainstorm. Video is a secondary case since most users will want to see them taking as much display resolution as possible (usually landscape).

Someone has mentioned controls of the media application through hardware keys and what consequences this have for portrait mode (see also http://maemo.org/community/brainstor...n_when_locked/ ). You can control the volume with +/- keys even with the display locked. For more complex operations, the system actually assumes that you have headphones with such keys integrated and much more reachable than a device in your pocket.