you're not having "problems" because the ECU is playing safe and keeping your engine from blowing up
also, there are weird cases that throwing on a header won't trigger a CEL at all (like UPSman's car)... what the determining factor is the 1st and 2nd O2 sensor readings... they can't be the same, and they can't be radically different from each other either... so there is a threshold/tollerance in the ECU's programming that "logically" determines if the sensor is "bad" or not... from what I understand, if the sensor readings are the same, then the ECU thinks the cat is bad or is not there... and if the readings between the 2 sensors are far off, then a sensor is bad... how the ECU determines if the sensors are functioning properly or not is by monitoring the voltage (after all, that's what the O2 sensor really outputs anyway)... NORMAL sensor readings should go from low voltage (about 0.5-1 volts) to high voltage (4.5.4.9 volts or so)... and back again over and over... it should never hits 0, nor hit 5... it should never stay at a constant voltage either... when both of those conditions occur, the ECU determines the O2 sensor is bad
this is standard practice on ALL cars on the road today... this is NOT a mazda specific thing