I think you might have it backwards (at least for people like me)
I don't associate old games with bad graphics at all, because at the time I played them, they had good graphics. So the thing that remains are the feelings I had playing the game, I remember feeling good about the graphics, so they were fine.
Personally I don't care for story at all, I refuse to follow any story and just care about gameplay mostly, in especial: how much does the game allow me to craft something interesting with its mechanics.
I think there is an easy case to be made that what lacks in modern gaming is good mechanics/gameplay, and they buy us out with story and graphics.