The surprising thing about the Aero engine market is not how GE did so well, as much as how Pratts lost it.
Pratt arrogance played a big part in their loss of market share - their customer support really suffered in the late 1970s and early 80's (coincidentally corresponding with when my propulsion career started). Pratt used the JT8D as a cash cow to finance the JT9D - shortly after I started work, one of the old timers showed me a plot of the cost of spares for the JT8D - there was a noticeable jump in the cost of JT8D spares every time they launched a derivative of the JT9D. It got so bad that I recall Pratt buying big ads in Av Week in the mid 1980s after they lost several big campaigns to GE for traditional Pratt operators. The ad was basically a mi culpa - accepting that Pratt had screwed up their customer service and vowing to do better. However for the most part, it was too little, too late - the damage was already done.
While the CF6 was certainly important to GE's future, it was the CFM56 that made GE the dominate force it became - it basically killed the JT8D, and it's massive numbers provided the funds for GE to develop the GE90 and GEnx. It got so bad for Pratt that they actually became a PMA supplier of CFM turbine blades.
Having spent considerable time working with Pratt, Rolls, and GE, GE can be a major pain to work with as a supplier - much more so than Rolls (it's been said both GE and Rolls will tell you to F-off, but Rolls somehow makes it sound polite
). But, when they have a serious problem, no one does a better 'all hands on deck' response to the problem than GE.