My best guess is that it has something to do with most render pipelines using CPU frame scheduling. Since the GPU can only process shaders, the CPU has to do e.g. input logic, reading textures from disk, etc. So in most engines, the CPU gives the GPU basic directions for each frame, and then the GPU goes off to process them while the CPU prepares the next set of directions.

If the CPU isn't fast enough, the GPU sits around waiting for instructions and it causes stuttering and FPS drops. If the GPU isn't fast enough, instructions from the CPU queue up and it causes input lag. To get around the input lag, most engines intentionally drop frames and decrease FPS (basically forcing the CPU to wait) in order to keep everything in sync.

Where VRAM comes into play is that that's where textures and other important data the GPU needs are stored. The CPU and GPU can actually both write to VRAM (though the CPU does so indirectly in most cases). Writing to VRAM is an expensive operation that benefits from parallelization, especially in the context of loading textures and cached shaders, therefore more CPU cores = better performance. Meanwhile, running out of VRAM usually causes the GPU to fall back to system RAM which is much slower, so more VRAM = better performance.

TL;DR The CPU runs the game logic and the GPU renders the result, so the GPU can only render frames as fast as the CPU can prepare them and vice-versa.

Edit: Since people seem unable to tell, I'm not a bot (obligatory fuck AI); sorry I use structured formatting tho ig ¯\_(ツ)_/¯