lomapaseo mentioned it early on -
Because of the large high-bypass fan (large relative to the core diameter), and its tip speed limits (acoustics, etc.), the LP shaft must turn a lot slower than the HP. This limits the amount of work a turbine stage can extract from the gas stream - ergo multiple stages are needed.
UNLESS - someone introduces a reduction gear in the LP shaft. Now the turbine can spin up to a speed where only 1 or 2 stages can do the work, still keeping the fan at a happy slower RPM.
Then, the only problem is the weight & complexity of the gears, and just one more "feature" to go wrong.
