I don't see any obvious reason for this. In fact, I think video could work well. There are certain sorts of interaction that just can't be easily articulated through text and static images (animations being one).
That being said, there are a couple of caveats to raise. Firstly, videos probably won't get watched that often. I don't have any stats from the SE sites which use vids, but watching a video means making a much longer commitment of time than simply reading a post. If the video's content could easily be transcribed, that does mean the content gets effectively 'lost'. It also creates a minor SEO disadvantage.
One way around video-only answers ('see 0:45 for the solution') might be to push users to only include videos with substantial textual content. That could mean disabling videos until a character count has been reached (sucky), or providing helpful tooltips when a user tries to submit a video-only answer ('If you can provide further textual details, more people will be able to discover your answer through search!').