There is a rationale behind using animated gifs vs videos vs screencaps vs text. In my experience, the most common way that documentation is written uses a combination of text and images (screencaps if digital). More recently we see that some people are using screencasts with or without narration for their documentation. Far less frequently we see text instructions accompanied by animated gifs.
As with all things, pros and cons exist for each of the usual methods. The text+screencaps method is popular for a reason but can’t quite convey action with their result. Videos with narration are great as a way introduce or teach a person about something but do not work as well as a reference tool. Additionally, unless the video has captions it becomes inaccessible to some disabled people.
My preferred method is to combine text with animated gifs. It has the immediacy of video with the accessibility of text. One downfall is that fine-tuning gifs is perhaps more time consuming than screencaps or video (although probably comparable with editing video…). Another is that gifs auto play and this can be irritating or outright harmful for some disabled people.