Sudden outbreak of common sense.
SpaceX is going "public" with only 4% of the stock being sold to outsiders. The S&P 500 requires a 50% public float. That may disqualify SpaceX for a long time.
Although GOOG and META are listed, despite control being held by insider shares of a different class. There was a time when the NYSE did not permit companies with more than one class of stock to be listed on that exchange. (Except F, FORD, which predates the NYSE). That was lost some time around 1990 or so.