EGR and performance questions

I used to think that way too. And at WOT, full power/full load you would be right. Absolutely.
But you have to think part throttle. With say 10%,or 20%,or even 30% hot air going into the cylinder along with the fresh charge it drives the mixture into a state of excitement, and homogenizes the mixture into a frenzied state where all/most of the charge will participate in the combustion process. Remember at part throttle/low rpm, and without EGR, the fresh charge is not very dense, and the molecules are/may be, spread all over the place, and they may not all be willing to burn in a 2/1 CR state. Perhaps some gas molecules will be trapped in places where they cannot find oxygen. Perhaps some will be stuck to relatively cool surfaces. With the hot EGR agitating all the molecules, the gas ones are more likely to find the oxygen ones, with which to react, and drive the piston down.
And the fewer unburned gasoline molecules passing out the tailpipe, the better. I mean, somebody paid good money for those molecules.