I undersand that the heated intake air will burn more efficiently with the fuel and thats why recuperators increase efficiency. The part i dont understand is that if efficiency is going up, why isnt the power output also not increasing along with efficiency? For example if we used to make 500hp from a free shaft gas turbine by using 100x amount of fuel and then we add recuperator and again add 100x amount of fuel, wouldnt the engine now make much more power than the original 500hp with the now more efficient combustion thanks to the recuperator? Is there a limitation in oxygen rich air supply like in piston engines so that we cant add as much fuel when there is a recuperator added? Or is this caused by some reason releated to the turbine itself and its ability to extract energy from the exhaust flow?

I understand that the heated intake air will burn more efficiently with the fuel and that's why recuperators increase efficiency. The part I don't understand is that if efficiency is going up, why isn't the power output also not increasing along with efficiency? For example, if we used to make 500 hp from a free shaft gas turbine by using 100x amount of fuel and then we add recuperator and again add 100x amount of fuel, wouldn't the engine now make much more power than the original 500 hp with the now more efficient combustion thanks to the recuperator? 

Is there a limitation in oxygen rich air supply like in piston engines so that we cant add as much fuel when there is a recuperator added? Or is this caused by some reason related to the turbine itself and its ability to extract energy from the exhaust flow?