As you have already in your question:
No, it is not possible to unvote or change your mind unless the post has been edited. This is due to questions as like to answers.
If you really want to change your mind and vote, you have to do a substantial (aka useful) edit to this post. Because then this post has been edited...
Usually there is a small amount of time after initial vote, where you can unvote. That means, during this time you can click again and your vote is gone. But I don't know how long this is.
Regarding the fact that this is a general feature for all SE-sites, your questions is "better placed" at SO-meta. And if you search there, you will find some long or short discussions.
