While it would be nice to have the option to add a GIF profile picture in Steam, and as a person who loves to use GIF profile pictures wherever and whenever possible - my Discord is a great example of this - I don't think it would work as Valve have already employed a 1MB upload limit and so then GIFs would have to be really low-quality.
Adding to that, GIFs would appear extremely small, and when viewed in a leaderboard such as Team Fortress 2, a lot of animated GIFs at once is a lot of processing power.