Based on this fuel flow chart, why isn't it more optimum to remain at an intermediate altitude rather than climbing?
When airplane mass, altitude, N1 (engine spool speed) and Mach number change together, it is very hard to come to a meaningful conclusion what is better for fuel flow. However, you see that the grey boxes tend to show the smallest fuel flow and they sit at the upper altitudes, so altitude seems to help. Going above 90% N1, however, seems to increase fuel flow again.
With increasing altitude, the flight Mach number needs to be increased to keep indicated airspeed constant. I expect that the chart lists trim points at or near the optimum polar point for cruise, at least that is what the almost constant indicated airspeed for each mass suggests. With increasing Mach, drag goes up but so does the distance covered per time, so there is again an optimum where the transsonic drag increase is still tolerable and outweighed by the higher speed over ground.
Therefore, higher flight speed is one reason why airliners like to climb to the tropopause. But there is more:
The thermodynamic efficiency of a heat machine grows with the ratio of temperatures in its thermodynamic cycle. Since the lowest temperature is determined by outside air, and outside air temperature drops with altitude while the top temperature is limited by the engine's materials, flying higher improves the thermodynamic efficiency of the engines.