It's rendered by your browser so you get properly subpixel-hinted text instead of the horrible, blurry, compressed screenshot effect a video or gif gives. Also it's more convenient to generate than faffing around with screencasting software.

Edit: well, not (lossily) compressed in the case of a gif but not as nice as text properly rendered for your display.

I'd guess it's the bandwidth and compared to a GIF, you can pause them. While it's not usual to copy text from it, I've done that once this month and thought it was neat to be able to do that. I do believe that they have an advantage over video/GIF.

It's definitely better than a GIF because you can seek forward. You never know when a GIF ends, and if you're distracted, you have to wait for it to loop back again.

Note that this is a function of the GIF viewer. An image / video viewer that can play GIFs with length, speed, and movement controls would afford this.

vlc seems to do this (Android version).

I'll grant that the usual methods of interacting with GIFs don't do this, and am not arguing that they do. But if you really want a specific functionality, you can look for a tool which might provide that.