It's been 5 years and there's still no progress on embedding YouTube videos. Is it not enabled because we are in the beta version and first we need to graduate or it doesn't matter?
Here are the list of the SE sites that currently support embedding YouTube videos. (All of them are graduated). My suggestion is to list examples of questions/answers like in this post from Movies SE where embedding a YouTube video would improve the quality of the question/answer.
The List:
It's also worth to mention some notes from this answer by Robert Cartaino:
Video is not searchable. I'd hate to see a potentially well-worded
question that describes the problem reduced to a video link asking
"What does this scene mean?" That will contribute absolutely
nothing to the future of this site. It's a black box to the rest of
the Internet.
We shall always try to avoid this type of useless content.