It's not true for unified systems, because they have no secondary RAM that could be used to extend the GPU memory.

It's pretty weird to insist on a counterargument that has no implications or consequences to the presented argument.

Yes, swapping is a bad idea.

Your second argument also falls flat, because the standard CUDA hardware setup doesn't use CXL so cache coherence isn't available. You're left with manual memory synchronization. Pretending that GPUs have cache for system RAM when they don't is pretty suspect.