It seems that this is allowed on a site-by-site basis on Stack Exchange.
Can we have it here?
I asked on meta.SE how we go about requesting embedded video support get turned on for The Great Outdoors. In theory, the results from turning this on should be a net positive.
StackExchange has support for embedding YouTube videos. This support is enabled on a site-by-site basis. Some SE sites are using it, but most are not. If we want it, we need to have that discussion and request it, probably at the main meta.stackexchange.
We have a lot of answers in which we guess at what might or might not work in any given situation. Sometimes that is the best we have, but the best answers would be proving the viability of the process. I see this as similar to providing links and citations for a researched answer.
And don't get me started on the questions about knots! We have an entire tag for knots, but rarely does anyone ever explain a knot in words in a way that I can understand. Pictures sometimes help if the knot is left loose and very deliberately in a picturesque way. Often I have to look up a video about the knot.
Most of the knot questions would likely be great candidates for videos.
I was told on meta.SE that animated gifs are an alternative. A gif is a picture file that supports multiple "frames" of an imagine which animate in a loop. That is true, it is an alternative.
In cases which could sorely use a video though, the gif is sub-par. Also, a long video might get too large to upload, as SE has a 2MB limit on images, but a video streams whatever data you need from YouTube as needed and so has no such limit.
There are a few cases where a very short, animated gif might actually work better than a video though, or at least as good. Some of my example Q&As above might work great with gifs, such as using a stick to hold down a snake.
A problem with the animated gif alternative
A video which contains content some users might not want to see should be optional to watch. ab2 pointed this out in comment in response to me using snakes as an example; lots of people cannot stand them.
An animated gif provides no way for a user to decide whether or not they want to watch the animation. It plays automatically and keeps looping back to the beginning.
Also, the animation starts right away and you might notice it when it is in the middle of the animation. I frequently have trouble watching them, as I have to watch several iterations before I realize what point is considered the beginning, then wait for it to get back to restarting again. Animated gifs are not nearly as user friendly in most situations.
Sue just brought up the possibility of videos being in a spoiler so that users could avoid them. Since an embedded video shouldn't play without clicking the play button, I think that applies less to embedded videos (though they still generally have a picture that represents them, like a cover picture); but this would apply much more to animated gif "videos".
If we can put a gif in a spoiler, that might alleviate unwanted content issues: just put a warning above then the gif of snakes, wounds, or whatever in a spoiler.
One answer on my question there suggested that the presence of videos can diminish the quality of the text, sometimes even eliminating text altogether.
enabling videos might allure people to make a video tutorial instead of writing a nice answer. This is already happening at so many places on the internet and I HATE it. Reading something is so much faster than having to watch a video to slowly get information I want.
This is a valid concern, and it also annoys me when I can find only videos about a topic and no text to read. However, I don't think this should stop us from using videos and text together for the best effect possible.
Another concern, posted in this answer on my question, is that enabling videos for a site apparently has a performance hit for all posts on that site, not just the ones which use video. The reasoning probably has something to do with how SE scans every post to see if it has embedded videos and then process the video link.
I recommend that we request embedded videos be enabled for "The Great Outdoors", as long as the aforementioned performance hit is not too bad.
I would assume it is a minor performance hit to the site, but I cannot know for sure. I have asked how severe the hit is and have been told that a discussion exists about that but that it would need to be tracked down.
If we are concerned about less effort being put into text, we could make a site rule that videos can only be made to augment text, not to replace it. Any videos which include a lot of talking about the information, where that talking has no textual counterpart in the SE post, would then need to be dealt with in some way, be it down-voting, closing, deleting, warning, etc..
If the performance hit is minor, I see no significant reason not to enable embedded videos. The minor drawbacks, such as less work put into text, should be outweighed by the benefit of a good video properly used. A picture is worth a thousand words, but a video can be worth a thousand pictures.