I'd be very happy to see the archaeology game go away. I find that I don't build theater squares much, and when the archaeology sites suddenly appear all over the map, I have dozens of tiles I cannot use unless I build theater squares, then amphitheaters, then archaeology museums, then archaeologists to remove them. To me, archaeology sites are a form of pollution (like in Civ2) and I don't like having to remove them to make the tiles accessible again.
On a larger level, the idea that digging up buttons and javelins and putting them under glass would help a civilization defeat its rivals is just beyond silly.
I think the promotion system of Civ6 should go. It's rigid and boring. Just seven options, and only two or three available at any one time? At most there are two different pathways for most units (a defensive path and an offensive path) and for some units, like ranged, one pathway is clearly better than the other. As is the case for SO MANY THINGS, I don't know why the Civ4 promotion system was abandoned. It was so fun to build different units with different abilities - some super medics, some all-around strong units, some specialized for attacking cities or working in jungles or hills. I suppose that the human player could exploit the system better than the AI can, but that's true for many systems; that never stopped the developers from implementing things the AI couldn't handle.