Unity supports 8k by 8k textures now, so you could use that. Still, even a single 4096x4096 RGBA32 texture is 67 megabytes of GPU memory. If you go to 8k by 8k you are now going to be using 268 megabytes. I suggest an alternative approach. Round up your artists and fire them for being dumb.
There are plenty of ways of using sprite animations though. First, you could stick to Unity's sprites for this -- UI2DSprite can draw them. Unity will then be responsible for creating atlases for you. Another alternative is to not just use sprite animations, but actually do sprite blending. Ie: instead of swapping sprite A to sprite B, blend from A to B instead. This will give you very smooth transitions. Third option is to split up your sprites into components. For example if you have a sprite that's a 256x256 square that spins around and the reason you can't shrink it down is because it has a fine pattern in it, you can use a sliced sprite to draw a rectangle, and a tiled sprite on top of it to add the pattern to it, separately. You can even write a shader to do blending, respecting the first sprite's alpha, if you're inclined.
Anyway, to sum it up -- there are plenty of smart ways to go, if you're clever about it. Using more memory is not one of them.
