I am against it.
While the implementation is already present as it is used on other sites, it will add considerable load time to the page itself. We are already loading one of the heaviest extensions possible, i.e. MathJax. For especially heavy MathJax sites loading already takes a very long time. Adding to that an implementation that further increases this time is not desirable. The sites that have it enabled don't use MathJax so that is less of a problem there. Apart from that, for example in movies.se you need the player because you are referring to a certain clip.
On chemistry.se the answer should be self-contained. That does in principle mean that anything important in the video should be written down as the answer. If the answer consists only of a youtube video, then (almost) always it will be deleted as a link only answer.
For me personally I do not see the necessity or the benefit. If you would like to include an animation of sorts, you can use animated gifs.