Animations using code are always potentially a security risk. I would imagine the development team at SE would be reluctant to open another potential attack vector set into their servers. This would be a code source and library set they do not directly control, so it is a problem. If you want to put it simply, the more more hooks you put on the wall, the more likely someone will hang something you don't want there. It's worth pointing out that the relatively simply image format standards and libraries do have to be regularly patched for security vulnerabilities. Flash animations largely fell out use because they were a constant source of such worries and Java Applets died for similar reasons. As a software developer in the past I like coding, but I am also very conscious of the security concerns source code of any kind raises. Sandboxes designed to contain these things are found to have leaks all the time, so be wary of this approach.
Animations (like images) do not parse nicely and efficiently into a search database. One of the reasons we actively discourage images of text and equations is that they cannot be searched for properly. There is also a tendency for people using images to rely on the image to tell people what the question is and omit even minimal text. Your own argument for using would suggest that people would do exactly that - post an animation and omit the vital text (and Mathjax equations).
I am particularly concerned about this last point. I am also of the opinion that e.g. two images before and after something, would be far more compact (in bandwidth terms) and just as clear (if not clearer) for explanation purposes.
Also note that if the poster needs to ask a question about some conceptual issue, it's just as likely there own confusion means they post an animation that does not clarify the issue at all. Making a post becomes as much a task focused on creating a graphic as it does about the underlying conceptual physics problem. That is a diversion from what the question asker needs to focus on.
Animations also take up space. While many people are used to and take for granted access to high speed broadband and wifi, this is not at all as widespread as it may seem to some people. Requiring (relatively) large animation files to be viewed to just read a question is going to present significant problems for many of our members. What is trivial for someone comfortable off living in a high density population center will be quite a different matter for people who regard high bandwidth telecomms as a luxury. Many people are also limited by bandwidth capping by ISPs). Animations also use up battery life on devices where that is an issue and, again, not everyone has the luxury of e.g. phones with large batteries.
So all in all I think using animations is a very bad idea.
On the other hand writing out the problem with text and mathematics may not be as flashy as an animation, but it will focus the mind of the person asking on the question they want to ask and the mathematics itself. From my own experience in university I would say that writing out my own notes was probably the number one way I learned things as I had to structure my ideas to write the notes. Just having to do this would often allow the concepts to "slot together" and give me the conceptual structure I needed.
So I think animation are not a constructive solution and as much as anything else are a diversion and resource hog.
That's my ten cents.