I was working the 777 at the time the 777-300ER/GE90-115B was launched. I don't think anyone at that time ever thought the program would enjoy anywhere near the success it has achieved.
Boeing was looking at what was called a "thrusting APU" as an alternative to development of a new 115k thrust class engine - something that would automatically kick in if an engine failed during takeoff. At the time I joked that all we really needed was a JT8D as an APU
. I found out later that wasn't too far off what was really being proposed
At that time, while Pratt, GE, and RR had similar market share on the 777, the Trent was emerging as the dominant engine. While all three engines were 'new', the PW4000/112" was a relatively small upgrade of the PW4000/94" on the 747-400/767 and PW4000/100" on the A330. Although the Trent 800 shared architecture with the RB211, it was largely a new engine, and the GE90 was a totally new, pushing the state of the art, engine.
The result was, while the PW4000 had an early reliability advantage, it paid a price for it's relative lack of new technology compared to the others, and GE's paid a big reliability price for it's new technology. The Rolls Trent appeared to have found the happy middle.
That all changed with the GE90-115B. GE had been working hard on the issues that had plagued the early GE90 engines and made numerous improvements while the -115B was being developed. The end result was an engine that could produce the same amount of thrust as the Redstone rocket that launched Scott Carpenter in the USA's first manned spaceflight, with impressive fuel burn and reliability.
When launched, best case estimates were that the GE90-115B would split the 777 market with the Trent 800 (with PW4000 becoming something of a bit player). In fact, Boeing confidence in the 777-200LR was so low that, in the aftermath of 9/11, the 777-200LR was shelved for ~2 years.
What no one really foresaw was, the combination of fuel burn, reliability, and flexibility made the GE90-115B/777-300ER/200LR a world beater - basically killing the passenger version of the 747-400 in the process. The GE90 has well over 90% market share on new 777's, and Boeing is literally building 777s as fast as they can - originally designed for a max 7 airplanes/month, they're now at 8.3/month and basically sold out for the next 5 plus years.
BTW, for the 777X, although the aircraft will be larger and carry more payload the same distance, the combination of better fuel burn and lighter materials mean that the 777X engine will actually produce less takeoff thrust than the GE90-115B