EGR's typically do not operate in two ranges, Idle and WOT, and of course only operate when the engine reaches operating temperature. They operate at cruise. When cruising at part throttle max HP is not a concern. You only need enough HP to maintain speed along with light or moderate acceleration. So, a loss of HP at cruise should be of no concern. Max HP is created at WOT when the EGR is not activated. Does anyone care about max HP at cruise? And if the EGR is not functioning at WOT then does it effect ET of max HP? No,
As for pumping losses, the EGR lessen pumping losses by effectively opening another port to atmospheric/or near atmospheric pressure (a big vacuum leak) without the oxygen to destabilize the AFR.
The inert air (dead air) partially fills the combustion chamber thus allowing for a smaller combustion while maintaining the cylinder pressure.

If you've ever driven a throttle cable operated EGR equipped car on the highway, without using cruise control, then you may notice having to reduce the throttle position to maintain and not exceed your desired speed. That's the EGR coming in. The EGR reduces the amount of 02 to maintain cruising speed, thus reducing fuel consumption, The EGR makes the combustion chamber effectively smaller and the inert air cools the combustion; it's a smaller combustion with less fuel, less 02 yet maintaining cylinder pressure.

When a technician sees a car with a detonation complaint and fuel economy complaint then one of the first things he needs to confirm is EGR function along with carbon buildup.

Now, would installing an EGR on my car be the first thing I would do to solve a high compression/detonation issue? No, probably the last thing I would do because they can be problematic, but they work and it doesn't effect WOT HP or ET.

Respectfully.