In one of my recent questions, I used two animated GIFs to explain my issue, which saved me a few sentences of explanation (in my opinion, the GIFs worked a lot better).
However, HTML5 videos are much better than GIFs. The first paragraph on the GfyCat about page talks about the benefits of HTML5 over GIFs.
Personally I don't see how those animated GIFs improve your question. They're rather annoying, and static images of the result would serve perfectly well in demonstrating what you're talking about. This is why animated GIFs are discouraged greatly, and also why users generally frown upon the idea of allowing videos - a lot of users would abuse the feature to include information that simply is not needed.
Even with the inclusion of images, your post should be able to stand alone. Images should always be accompanied by text that can also describe the problem. Images are meant to be provided as a supplement to indicate "this is what I'm describing if you're not getting it" - not as a substitute.
Further, we want users to get to the point. Video and animated GIFs require users to sit through some long series of events in order to figure out what is going on. No one wants to do that. Text is straight to the point, and can be skimmed for relevant information - so even if a user includes a bunch of irrelevant stuff that doesn't help their question, users can still quickly pinpoint the problem. Animated GIFs don't let you skip around at all (or even pause for that matter), and even with videos it's still a process of randomly selecting arbitrary points and hoping you hit some key piece of information.
Videos are just plain not useful on the majority of our sites. The length that they would need to be in order to actually be useful to the post is so small that it doesn't make sense to even have it (bringing me back to your case, where only the single frame is even necessary). Sites which do have a need for longer videos, such as Arqade, already have a feature available for rendering videos inside a post.
