I think this was primarily about speeding up the measurement time. With just two electrodes you had to wait for the device to achieve equilibrium with the material being measured. If the concentration of oxygen on the probe side of the barrier was higher or lower than the material side you would get false measurements, particularly in low oxygen scenarios because you have oxygem trapped in the probe.

By keeping the state of oxygen inside the probe constant and replacing consumed molecules you now can measure almost instantly.

Because then it doesn't alter the side of the membrane where it does the reading (plus one minus one equals zero). That makes the measurement more accurate.