Cross platform compatible
Using html in types like video makes it not really compatible with other platforms other than browser. In fact it is a bad format for browser too, it has assumptions about rendering and forces to use iframe to avoid xss.
This spec pre-dates HTML5 video being widely available, so is based on the way all video content was delivered at the time; Flash, Silverlight or Quicktime.
The oEmbed spec was written in March 2008, but support was added later to Safari & Firefox (June 2009), Chrome (Oct 2009) and IE (March 2011). It also predates the iOS app store by 6 months, so mobile support was not originally a goal.
Adding a new content type to oEmbed is not out of the question, if there is enough demand for supporting it.