AIUI due to the original 737 having a narrow diameter turbojet they didn't have to make the undercarriage that long. Consequently when they came to build the 737-300 and later it was difficult getting a turbofan under the wing, hence the flat bottom on the engine cowling. This meant the engine suppliers had to make a special version of the engine with a reduced diameter fan section which I'm guessing contributed to RR's lack of interest at a time when they were recovering from the RB211 bankruptcy fallout.
With the A320 wing being a sensible distance off the ground this wasn't a problem and RR were part of the International Engine Alliance which produce one of the engine options for that, and are still a major supplier to it.
It has been said modern aero engines are like the razor blade business, you make a loss on the engine but make it back selling replacement blades!