The recirculation will allow hot air back into the combustion sequence.
Without EGR, the engine will be fuelled purely by fresh air, meaning cool air.
The EGR system is a waste of time and money in the UK as NOx (the gas it is intended to reduce) is not tested in the MOT.
I thought because the exhaust gas is inert means that it doesn't combust so therefore that's where the temperature is kept down (and power
)?
OK - I assume you have read a textbook on this recently, because it is true that lean intake charge has a higher specific heat ratio than an EGR mixture. To answer the power issue, a reduction of specific heat ratio reduces the amount of energy that can be extracted by the piston.
Theory is theory, practice is practice. Modern engines don't run lean or rich (unless they are wanked). They run as best as they can for the environment they are in. If it's hot outside, you wear a T-Shirt. If it's cold, you wear a jumper. The ECU does the same thing, and supplies the correct air to fuel mixture.