I know how the EGR works in relation with the ECU...and, it's obvious that you do not. Once again, misinformation from a person that "heard" pure BS and has NFI of how it really works.
1) The EGR reduces combustion gas temps...this in turn makes detonation less likely. There was a marked difference on my motor...50-100 deg C EGT drop due to installing the EGR to pass emissions. It's still on the motor because of this.
2) The USDM ECU is tuned for the EGR...it's fuel and timing maps are based on it being present on the motor. Where this comes into play is at high engine speeds (3000-4000 rpm) under load...you risk detonation as a result.
3) The difference in HP due to "exhaust gases taking up space in the cylinder" is very minor. You could dyno any car with and without the EGR and there be a 5 P (or less) difference. I'd much rather increase boost and have less to worry about detonation wise.
4) The EGR reduces one of the most noxious emissions gasses there is...nitrogen oxides. If you take it off (along with your CAT), you should be doomed to breathing crappy air the rest of your life and fully experience the health issues that go along with it.
5) If you making a track only car, removing the emissions equipment is fine...you do need to pay attention to what the ECU does with it gone (especially the EGR). If it's not going to be a daily driver, you can disregard #4 above
I'll tell ya, I despise the "clean up the engine bay crusades". Guys start yanking "unneeded" parts off the motor with no idea of why they are there. The result is multiple problems down the road with idle, running rich, misfires, etc, etc. Do what you want, but screwing with an EFI motor without knowing exactly what you're doing will result in you working on it more than you drive it...all to solve self induced problems.
BTW - I hope you have very deep pockets...attaining 700-800 HP is going to require a boat load of $$$. You will have to completely re-build the bottom end, extensive head work, big turbo, IC and associated piping, stand alone EMS...this is just for starters. Not to mention what you will have to do to the drive train. Based on your above posts, this should be interesting