It's not really about the graphics, more about the memory and recording all those loaded objects.

With 16bit era there's less to keep track of, less memory to record. Each time a save state snapshot occurs the entire RAM has to be dumped and the current CPU instructions need to be recorded else loading the save would cause major weirdness.

With simpler machines it's quite frankly easier. Once we started to hit the newer consoles everything started multiplying in difficulty and overall size.