Crystal Palace spent the last five of these nine seasons in the Premier League, from 2013/14 to 2017/18; the four before were outside it. Against City they won once, drew once and lost eight, taking four points. Take City out and all four go.
That shapes the whole run. In the three seasons Palace took nothing off City, they move up: 11th to 10th in 2013/14, 15th to 14th in 2015/16, and 14th to 12th in 2016/17. In the two seasons they did take points, those points cancel the free place, and Palace finish exactly where they did for real.
No fate is in play either way. In the rebuilt tables Palace never come closer than six points to the drop, or 19 points to fourth. In 2013/14 the rebuilt season still includes the game in which they came back from 3–0 down against Liverpool; that game never involved City, so it stays.