Animations and mesh LOD and etcetera are too small to be request real time on the fly, these are things that need to be prepared beforehand.
You're looking at the wrong end of the stick. A interactive feature, whether that's a weapon or something interactive like a cupboard, comes with a wide range of assets that are required for it to be interacted with and dynamic. Many common forms of these assets are loaded all the time. But finer grain control of memory allows more data to be loaded and unloaded on the fly. As a result, more memory can be put towards the fidelity of assets that are currently needing.
A great example is a player weapon in a third person game. It might just be holstered on the player character's back, but all the associated anims (movesets, attacks, impacts, interacts, etc), audio & VFX will be loaded whilst its there. With much faster I/O you can bring lots of that data within the time it takes the character to unholster that weapon, whilst clearing out the data it replaces.
And right now something like a basic idle anim might only be a few 10kb..., but anim requirements are about to go up: more detailed rigs, animated textures for cloth & skin movement, extra anims for more accurate blending & variety. A full anim set
As for Mesh LODs, a really detailed mesh (100,000+ polys) with multiple LOD levels can take up over 100 of megs of space. Not only will that detail be going up again on the next-gen, but higher resolutions can require more mesh LOD levels (And texture mip levels) to keep performance and quality balanced. So again, further fine grain control here can be beneficial.
Remember that with this gen, the amount of available memory is not increasing at the same rate as it has on previous generations. More efficient use of memory is a must if those CPUs and GPUs are going to be pushed appropriately and visuals noticeably improve.
As for "prep", what "prep" are you talking about exactly?