If you see the drag vs TAS curve, we want the best TAS/DRAG.
Now as wt reduces in cruise due fuel burn, we have two choices
1. Reduce IAS by reducing thrust (hence fuel flow). The TAS reduces BUT Drag is propor tional to IAS2 , hence better TAS/DRAG. (constant altitude method)
2. As wt reduces start climb such that TAS is constant or reducing to maintain constant MNo. whilst in this the TAS is reducing but the relationship between IAS & TAS is such that IAS reduces to effectively reduce DRAG much more hence giving better TAS/DRAG. (climb cruise method)
So better TAS/DRAG in climb cruise method
You can check & confirm with the RAF AP3456.. good book.