If you're recirculating exhaust back into the engine, you're able to attempt to reburn any fuel that wasn't burned on the first pass
That's not what EGRs do.
EGRs take exhaust, which is relatively inert (combustion having already taken place) and injects it into the combustion chamber to lower combustion temperatures. The reason you want low temperatures is that NOx (nitrogen oxides) form at high temperatures.
"In internal combustion engines, exhaust gas recirculation (EGR) is a nitrogen oxide (NOx) emissions reduction technique used in petrol/gasoline and diesel engines. EGR works by recirculating a portion of an engine's exhaust gas back to the engine cylinders. This dilutes the O2 in the incoming air stream and provides gases inert to combustion to act as absorbents of combustion heat to reduce peak in-cylinder temperatures. NOx is produced in a narrow band of high cylinder temperatures and pressures.
In a gasoline engine, this inert exhaust displaces the amount of combustible matter in the cylinder. In a diesel engine, the exhaust gas replaces some of the excess oxygen in the pre-combustion mixture.[1] Because NOx forms primarily when a mixture of nitrogen and oxygen is subjected to high temperature, the lower combustion chamber temperatures caused by EGR reduces the amount of NOx the combustion generates (though at some loss of engine efficiency).[2] Gasses re-introduced from EGR systems will also contain near equilibrium concentrations of NOx and CO; the small fraction initially within the combustion chamber inhibits the total net production of these and other pollutants when sampled on a time average. Most modern engines now require exhaust gas recirculation to meet emissions standards."
That's traditional "external" egr. Many newer engines have an "internal" egr implementation, which just changes valve timing so that some amount of the combustion products are never evacuated from the cylinder in the first place. With cam phasing becoming commonplace, internal egr can be implemented without adding any additional parts, and is thus cheaper. So the "recirculation" part of egr is becoming more and more of a misnomer.
Personally I like internal egr because external egr systems have a tendency to clog in either the passageways or the solenoid controlled valve. EGR valve sticking is a common cause of cars stalling when slowing to a stop after cruising at medium-high speed. And even without the stalling egr is a common cause for check engine lights and smog test failures.
That's not what EGRs do.
EGRs take exhaust, which is relatively inert (combustion having already taken place) and injects it into the combustion chamber to lower combustion temperatures. The reason you want low temperatures is that NOx (nitrogen oxides) form at high temperatures.