there are TWO temperatures
there are two different temperatures to be considered.
1. Burning temp or flame temp. This decides the Carnot efficiency, the other factor being the exit temperature. (temp difference in Kelvin divided by max temp). this is the efficiency realised by the ability to burn fuel at a high temp and expand the air by accelerating it thereby cooling it. The more you can accelerate it down the jetpipe, the more thrust you get, the lower the temp and the higher the thermal efficiency.
2. EGT is not the same as exit temperature, though it obviously IS corelated. There is a limit to the temperature that turbine blades are designed to withstand, and this decides how much work can be extracted, and how much combustion temperature can be tolerated. Workarounds are to have turbine cooling systems. With improvements in materials (crystal blades etc), higher temperatures can be designed.
The objective of high bypass is to enhance PROPULSIVE efficiency by handling a larger mass of air at lower acceleration rather than a small mass of air at higher acceleration, which is different from Thermal Efficiency. Higher flame temperatures improve the efficiency of the core engine which in turn improves overall efficiency. Overall, you get a higher Compression Ratio, improve thermal efficiency and burn less fuel. Is there an upper limit if we can keep improving the metallurgy of the blades.? This would be the limit of temperature at which the fuel could burn without losing its chemical properties of calorific value and stability (?)
In short, you ARE getting more out of the same amount of fuel, but it's no secret weapon. Isn't that why engines are so bloody expensive..?