"EGR adds to the total amount of gasses being pumped through the engine therby increasing pumping losses"

This statement is incorrect. "Pumping losses" mean the amount of atmospheric absolute pressure (energy) that is wasted sucking air past the throttle plate. So for example a Diesel engine has close to zero pumping losses.

From Wikipedia: "A properly operating EGR can theoretically increase the efficiency of gasoline engines via several mechanisms:
Reduced throttling losses. The addition of inert exhaust gas into the intake system means that for a given power output, the throttle plate must be opened further, resulting in increased inlet manifold pressure and reduced throttling losses.[7]

A properly operating EGR can theoretically increase the efficiency of gasoline engines via several mechanisms:
Reduced throttling losses. The addition of inert exhaust gas into the intake system means that for a given power output, the throttle plate must be opened further, resulting in increased inlet manifold pressure and reduced throttling losses.[7]
Reduced heat rejection. Lowered peak combustion temperatures not only reduces NOx formation, it also reduces the loss of thermal energy to combustion chamber surfaces, leaving more available for conversion to mechanical work during the expansion stroke.
Reduced chemical dissociation. The lower peak temperatures result in more of the released energy remaining as sensible energy near TDC (Top Dead-Center), rather than being bound up (early in the expansion stroke) in the dissociation of combustion products. This effect is minor compared to the first two.