The TRENT comes off wing in any combination of six "Modules". 1-5, and eight.
The Modularity was highly touted; wags insisted it was necessary due the need for TRENT's bits to be in the shop. Not too far wrong, v/v the 9.
Modularity saved money, a promise Rolls made to its clients. It saved so much, Rolls took the engines back (on "Total Care"), and advantaged themselves of what they thought would be a profit tool. It was, and it wasn't.
So you are correct in saying the Tri-Spool is more complex, (more parts, more pieces) but it is the separation of twin spool shafts into halves that make it easier to r/r, and more susceptible to service isssues relative to joints, mass, and metallurgy.
imo
(I see you changed Turbine D's qualifier "efficient" to faster. Caught that,)