You got it slightly backwards but you knew what you meant to say.
A reduced thrust takeoff BURNS extra fuel (longer to accelerate, less efficiency of the engine at lower thrust) in exchange for dramatically extended engine life.
Max thrust saves gas, but turns your engine into a pile of rubble in no time at all. As the engine degrades efficiency will go down and fuel consumption will increase (probably where the theory that reduced thrust saves fuel comes from, then engine will stay in pristine most efficient shape longer)
So on a leg by leg basis, just to rehash, reduced thrust burns more fuel. BUt on a const basis over the long haul reduced thrust saves buckets of money.
Cheers
Wino