Not completely impossible. There's a way around this problem, but it's tedious.
Hack the garc containing Pokemon models, and clone the costume files over other Pokemon files.
(Let's say, replace the first few Pokemon with the Pikachu costumes)
Then load the garc using layeredFS, salthax, or luma's layered loading.
That's how I managed to take screenshots of out-of-Alola-dex Pokemon for SM for bulbapedia.
1. Get citra + plus the game (don't ask where to get roms) or a 3DS with capture card + the game or NTR CFW to stream the gameplay to your computer.
2. Complete the Pokedex (hacking or otherwise)
3. Enter the "viewing" mode of Pokedex, zoom all the way out (the L and R bumpers/buttons of the 3DS controls that.)
4. Record video of the animation. One video for front, one video for back (my obs settings if you use that program to record desktop video)
5. Splice the video into individual picture frames (with sites such as ezgif)
6. Manually remove the background from every frame, and remove repeat/looped frames.
7. Apply partial transparency to stuff that has transparency, if necessary. (explainer/example thread)
8. recompile the frames as gif (or apng if it has partial transparency)