You’re not missing anything. Animations are specific to a single skeleton asset. If you want to apply animation assets that use one skeleton asset (e.g., the UE4 skeleton) to another skeleton (e.g., the Mixamo skeleton), they need to be duplicated first. An animation asset can’t contain data for more than one skeleton asset.
But you can have multiple skeletal mesh assets that use the same skeleton asset, which is probably the best way to go in typical cases. Any animation that can be applied to one skeletal mesh can also be applied to any other skeletal mesh that uses the same skeleton, although you might need to mess with the retargeting settings to prevent weird behavior on skeletal meshes that have very different proportions from the original.