And to illuminate further on Black Swans point- the 300ER and 200 F and LR have GE-90s because no other production engine produces that amount of thrust.
Only because....
Trent 8104.
In 1998 Boeing proposed new longer range variants of the 777X. Taking advantage of the Trent 800's growth capability, Rolls-Royce designed and built an improved engine designated Trent 8104, which was later scaled upwards to the even larger 8115. This development was the first engine to break through 100,000 lbf (440 kN) thrust and subsequently the first to reach 110,000 lbf (490 kN). However, GE Aviation former president James McNerney (now Boeing CEO) successfully offered the aircraft manufacturer up to $500 million in money to develop the 777X in exchange for exclusivity in powering the family. Boeing agreed in July 1999 to such a deal with the GE90-110B and GE90-115B to be the sole engines on the long-range 777s.[15] This resulted in the 8104 becoming just a demonstrator programme, despite setting further industry firsts for thrust levels achieved and the first to demonstrate the use of a fully swept wide chord fan.
From an informed source.
Ok, its wiki but it is a story that this side of the pond at least, is very well known.