Embedded YouTube videos are possible on a per-site basis.
I think Woodworking is a good site to enable them on, for various how-to videos and such, which are plentiful on YouTube. It'll also make it easier for answerers to shoot their own videos and include them in posts.
I believe woodworking is a topic that is particularly well-suited to videos.
For comparison, here is the percentage of questions that have at least one answer with YouTube links on Woodworking compared to some of the other sites with embeds enabled (updated 2016-Sep-10):
SITE YT ANSWERED QUESTIONS Movies 2391 12567 19.03% Music 848 8543 9.93% Woodworking 93 1217 7.64% Sci-Fi 2079 33874 6.14% Space Ex 250 4565 5.48% Gaming 2877 70736 4.07%
Doesn't really hold a candle to Movies, but still pretty comparable.