The cost of developing a new engine is huge. The GE benefit was that they had already done the ground work for an all new engine that could be tweaked to reach the thrusts required (115,000 and possibly beyond), while the RR Trent would need a whole new design to get to those thrust ratings. And in today's market, RR don't have the cash to invest in designing a whole new engine to compete with an existing competitor who has sown up an exclusive deal with the aircraft manufacturer.

It was never going to be economical to have two engine manufacturers competing for the 100K+ thurst requirements. The development costs would not be recovered for both and that would increase the overall cost of the aircraft purchase, making the 777 less competative against its rivals (A330, A340), which is why Boeing wanted a single exclusve engine supplier in order to keep the supply cost low.