The post cat O2 sensors don't provide any input for A/F ratios to the pcm. Only the upstream O2 sensors do. The downstream O2 sensors are mainly just for evaluating catalytic efficiency(if the catalytic converter is good or faulty). Removing the cat will throw a CEL but won't effect performance(due to that code/light). You can do the spark plug non fouler trick to keep this code/light from showing up and it works most of the time.
The main reason for doing it is so if ANOTHER code is thrown(say random misfire, emmisions code, whatever....) you realize it and can correct it. If the CEL is always on(due to the O2 sensor and cat converter removed) then you won't know when another code is thrown.
Breathing in and out is good enough for me.