heres the logical reasoning:
say you install a less restrictive exhuast on a stock engine. they engine will not preform as well that is the HP and torque will drop.
Because the engine is outside of it's stochiometric ratio. What is that? That's the chemically "neutral" balance of air/fuel ratio. It has been shown that engines produce maximum horsepower at 14.7:1 (air/fuel) by mass. The problem is that when you alter the backpressure of the exhaust system, the ratio will also be altered. If you reduce backpressure, the engine is allowed to flow more air out. More air out means more air in. If the fuel system is not compensated for the increased air mass, the engine runs lean. If the backpressure is increased, the mass of air leaving is decreased. Less air out means less air in. Again, if the fuel system is not calibrated for the change, the engine will run rich. and rich or lean engines do not preform better than and engine with a nuetral air/fuel ratio.
Ok, again from a "non-attacking" standpoint! :
I would totally agree with the theory of the increased escaping airmass causing the engine to run lean. It's the same simple reason that I have to "jet up" my bike and sled when we go from stock exhaust to aftermarket pipes. You're able to flow more air than the stock jetting can keep up with, simple as that. But definitely NOT from taking off your cats. There is not NEAR enough of a restriction change to cause that dramatic of an AFR alteration to take place.
In an FI motor, the same is true, but with a slightly different premise. Like I hinted above, the ECU is fully capable of adjusting for alterations in air mass. Otherwise, a car that ran right at sea level would be indriveable up here in Idaho where you can hit 8000+ ft on a highway (and vice-versa). On the same note, this is also a huge reason in which I had to get my computer retuned for the 39lb injectors that went in with the turbo. They're double what the stock injectors were (19lb), and that would be far, far out of the compensation range of the ECU. The O2 sensors would see the mixture super, super rich and not know what to do. It would cut the fuel trims back as far as it could, but there would still be too much flowing in for it to compensate.
Fuel trims! What's that?!? How the computer deals with the O2 sensors (in a nutshell). The computer is watching the front O2 sensors, comparing it to throttle load, and essentially deciding what the AFR (air/fuel ratio) should be. If it decides the mixture is lean, it increases the STFT (short term fuel trims - increasing ADDS extra fuel; negative would REDUCE fuel, for a rich condition) to bring the AFR back into line. Usually, the STFT's are constantly going from positive to negative, positive to negative. But, if the computer is constantly seeing the STFT's either dominantly positive (lean) or negative (rich), it begins to change the LTFT (long term fuel trim) curve to account for it. Once the LTFT curve is within a reasonable limit, this brings the STFT's back towards a zero increase/decrease and the positive/negative oscillation, which is what the computer wants. This discussion of backpressure causing problems goes back to about right here. What you are claiming is that the computer wouldn't be able to account for the airflow change with it's fuel trims. To a point, this COULD be true, but not simply from removing the cat's. The fuel trims can only account for so much, but that 'so much' happens to be quite a broad range. More than most normal car users could run into problems from.
As for air/fuel ratios and achieving stoic, I should post a video of my wideband gauge. It's very simple to see when the engine is seeking stoic (less than about 80% throttle) or when the motor pushes into boost and goes to (rich) 11.5:1. A motor makes basically the same amount of power at slightly rich as it does at stoic. Any dyno-tuning facility will purposely run the engine rich when going for peak power. Also, it's just safer - ie, less of a chance to burn the motor down or detonate it to death.
Overall, any exhaust you throw at an FI motor won't be out of the adjustability of the ECU. They're specifically designed to allow changes like this and be able to compensate. Massive changes in airflow (NOT adding a K&N, but rather something like boost) will achieve the same result as what this "loss in backpressure" is causing.
Do what you want with your cats. The engine will still run fine. You'll have a check engine light until you deal with the rear O2 sensors, but other than that, should be no problems. Except that the feds don't like it and they might want your money!
Welcome Visitor! Please take a few seconds and 
