So on a technical level i'm still left wondering.
At each RPM/load/throttle position/etc... the car is still getting the same amount of air, fuel, backpressure, boost, etc..., correct? If so, then it would only seem to be the rate at which the car changed RPM that was affected. This is due to a lower rotating mass, meaning less power is spent spinning the flywheel, and more power is delivered to the wheels.
Under acceleration, the amount of power required to spin the flywheel is miniscule compared to the power required to accelerate the car. Now what I mean is let's say under normal acceleration you can go from 1000 rpm to 2000 rpm in one (1) second (I'm using easy numbers, not necessarily accurate). In that time you've doubled the speed of the car--let's say from 10 mph to 20 mph--requiring significant energy to do so (lets say 200 hp/s). You've also had to physically accelerate the rotating components of the car: everything from crank, flywheel, driveshaft, axles, wheels, cams, etc... It takes some amount of energy to spin them from 1000 to 2000 rpm--let's say 10 hp/s.
Now you drop in your lightweight pulley. Everything in the above statement remains true, except the last sentence, where we now can say it took maybe 9.95 hp/s. So now you have an extra .5 hp/s that ends up going to the wheels--which means faster acceleration. So now you reach your 2000 rpm a split second earlier. But at each ecu clock cycle along the way, you had the same parameters being calculated since no extra air was getting in, or fuel, or boost, or anything like that. It just had to step through the tables SLIGHTLY more quickly, right? But i'm going to assume that the ECU operates at a frequency where it can easily handle stepping through tables at pretty much any rate you throw at it.
Even on engine braking, most of the energy doesn't go into spinning the engine components, but to drive the pistons up/down compressing air, etc... A perfect example is F1 cars. They have crazy light components, lower polar moment of inertia, but they still engine brake at almost 1g. So if problems dont come from accelerating, and they dont come from engine braking, i can only see two places left for problems to occur. Either applying the clutch in a situation where the RPMs were not perfectly matched, and perhaps putting the clutch in revving it or letting the engine wind down.
Is that where the tune comes into play? I'm trying to understand the mechanics of why a tune is required.