You can already do that by copying the embed code YouTube and other video sharing sites can give you (click the Share button, then Embed). While I do agree that this feature could be made more obvious, adding a BBCode button for it wouldn't make it easier to embed videos (it'd be roughly just as complicated, you'd just get the code from a different place) and would have to account for all of the different formats a URL to a video can have, which would make it more unstable than just copying the embed code from the video site.
Does anyone else have opinions about this or should I close it? My personal opinion that a BBCode tag wouldn't make this easier still stands. Should this decision be made final, I'd be open to somehow clarifying the ability to embed directly from YouTube and other sites.
I don't think we need this sort of custom embed option when Youtube provides a way. If we were a site that didn't allow HTML in posts then such a code would be useful, but since we do we can just use what Youtube provides.
Seeing as nobody has yet provided any arguments against copying the embed code from YouTube, I'm closing this issue. If you have such an argument, feel free to contact me so that I can reopen the issue.