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EGR is a mixed bag. Certainly, pumping losses are slightly offset by the current crop of EGR systems. Yes, timing can be advanced. Yes, compression can be increased (and still meet emissions targets).
But, when an engineer designs and configures an engine, having more advanced timing and higher compression does not directly correlate to higher efficiency.
Example, many experimental engines with high EGR flow rates require timing advances as high as 50 degrees BTDC, just to function properly. That's not good in any way. Rather than look at timing advance as "good", look at it as necessary under certain circumstances for proper operation. We NEVER want pressure increasing by much prior to TDC. Yet, that's exactly what happens with extremely high EGR flow rates.
Compression ratio's are directly related to efficiency. However, don't confuse the high ratio's used on modern engines with the advent of EGR. Remember, EGR generally does not flow at WOT and/or high power settings. Yet, that high compression functions just fine. EGR simply allows the use of high compression without exceeding oxides of nitrogen emissions.
What's possible with very high compression, very lean burn and moderately advanced timing without EGR is impressive indeed. Experimental air cooled aircraft engines (operated lean of peak EGT, with high compression pistons, 2 plugs per cylinder and timed for optimum efficiency) regularly achieve BSFC numbers well below 0.38 pounds fuel per HP/HR. Some brag about numbers below 0.35, on gasoline! EGR does not help in any way under these conditions.
There is much more, but those are the basics. EGR is generally not helpful or harmful in modern engines with regard to fuel economy.
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