The biggest reason to place them at the top or bottom is scanability. You can very easily glance immediately to the top or bottom of the player, regardless of the content, without a close look. If the buttons are in the middle you have to search for them.
Also as Matt Obee mentioned, it makes the most sense for the time bar to be horizontal (how time is generally represented in info visualization) so a vertical layout for controls is generally ruled out.
As for why is the bottom the most common position? I suspect it's largely because it's often where TVs present menus/overlays. Any sort of "pop-in" menu often appears at the bottom (like Youtube's controls).
I'm not sure there's a great reason for bottom alignment being the most common (though if you have a large TV craning your neck up is usually less comfortable than glancing down, an TVs are usually at or above eye-level), but it's now common enough to be a convention. Once something's a convention it's rarely worth challenging conventions without real data to support a change.