I believe that in some parts of Europe, the emissions inspection process requires the "sniffer" test to be performed within 60 seconds of starting the engine.
The air pump is there to accelerate the warmup process to accommodate this requirement. For all practical purposes, US spec cars could probably do away with the air injection pump altogether...
2009 ML350 (84K) - Family vehicle
2001 CLK430 Cabriolet (71K) - Wife's car
2005 BMW 645CI (124K) - My daily driver
2012 Mustang V6 (60K) - Daughter's car