In some turbopump designs, propellant is burned and used to power the pumps; then it is dumped overboard. This causes a reduced specific impulse, because not all all the propellant is expelled through the nozzle in an efficient way.
However, some designs don't dump any propellant overboard; for example, in a closed expander cycle, fuel is pumped in at an extremely high pressure, then expanded using heat from the combustion chamber / nozzle (which powers the pumps), and then finally enters the combustion chamber.
What I don't understand is how this could achieve less than a perfect effiency, since all the energy consumed eventually ends up going back to the fuel; an inefficient turbopump simply heat up the fuel slightly, and an inefficent turbine powering the pump simply means that less energy is extracted from the fuel in the first place. In the end, all that energy ends up in the combustion chamber.
Obviously, this can't be right, so what am I missing?