No it's memory as more objects you render need more space to hold thier data. Clearly you don't know much
There's a reason why gpu now have 8+go of vram to run on high settings
Hahaha, dude, I work daily with this stuff.
Let me try to explain it to you. LODs are not used to reduce ram usage, they are used to reduce the draw calls and polycount of a scene. When the player moves closer and a higher LOD pops, that higher LOD hasn't been loaded into ram then, it was already loaded (otherwise you would have insane amounts of stuttering).
For example the trees in the distance in, say, Witcher 3, are lower LODs in PS4/XB1 not because of RAM, because they are, most likely, literally THE SAME trees that are 5 meters away from you so they are already in memory, but to reduce draw calls and polycounts, and draw calls are one of the biggest CPU loads and usual performance bottlenecks.
Another example would be, say, a car in Forza. At lower LODs it will have not only a lower polycount but a lower amount of meshes as well.
Same with culling, the stuff that is not rendered is not loaded off the ram, it's just not rendered.
Lack of VRAM can be seen when a game stutters heavily due to not being able to keep all required textures at the same time or low res textures are seen while they stream in.
Obviously yes, in extreme scenarios if you are showing tons of unique assets in the same scene (something that very rarely happens in AAA games anymore, lots of assets are reused) you might have to cut drawing distance due to ram, but you will likely run into CPU bottlenecks before the differences in ram matter, especially considering we're talking about Jaguar.
Shadows could have better draw distances and higher quality though, as they rely almost entirely on GPU. SSAO could also be more precise and/or higher res. This is all assuming the same resolution though.
But LODs, tesselation, etc are not bottlenecked by RAM.