Huge file size, poor color support, no video controls. Gifs have no place on the web.

It is potentially possible for the browser (or an extension) to support the user using play/pause/rewind/fast-forward with animated pictures. However, I do not recommend GIF; animated PNG is better.

(But, I would prefer text-based documentation. You can still have videos or animations too if wanted, though.)

Actually, animated PNG has some benefits and some drawbacks compared to animated GIF. (You could try both and see which works better for the animation you are making, I suppose.)

But animated GIFs don't go at your own pace. Doesn't that annoy you sometimes?

I guess a video would do the trick though

Something taking over my interface and locking me into its narrative, explaining instead of showing annoys me 10x more. An animated gif can loop so I can watch it twice.

Problem with animated gifs is that they are not very efficient in terms of bandwidth, especially if you need them to show UI interactions (which means you need a high frame rate).

The word "gif" now means both the format GIF, and also any generic short, looping video on the Internet. As a result, you can just use a webm or other format, as Gfycat does, since it's highly compressible and no viewer actually cares about the underlying format, only the content.