I've done some pretty deep thinking about this "phenomenon" of the Phonic Wheel Relearn and, so far, the conclusion I've reached is this. The crankshaft and camshaft both have sensors which transmit a signal to the engine ECU every time they complete a 360 degree revolution. The crankshaft drives the camshaft via the timing belt and thus it's this relationship which determines the cam timing of the engine and therefore how well the engine runs. These are two completely separate things.
So the valve timing and correct running of the engine are down to correctly fitting the cam belt and it's associated pulley positions - It's the locking tools which let you accomplish this.
The relevance of the Phonic wheel relearn is that this teaches the ECU to accept that, when the relearn is performed, the angular relationship between the signal these two sensors send it is what is "normal". In other words, If we accept that the crankshaft sensor signal is the reference then the ECU is expecting to see a camshaft sensor signal on every second revolution of the crankshaft at a precise degree of angular displacement. If this signal arrives when the crankshaft is in any other position then the ECU will detect and compare this to the stored data and flag up the misfire code (which we know is a red herring) and light up the EML.
That pretty much sums up my own thinking on this also.
So if after the new belt is fitted, the angular relationship between camshaft and crankshaft is
exactly the same as it was before, then everything will work just the way it did before and no relearning is needed.
It follows from this that, if there are running problems after a belt change, the angular relationship between camshaft and crankshaft must be different than it was before you started. If this difference is small, the engine will run without destroying itself; if it is very small, but not quite good enough to run properly, then a phonic wheel relearn might do the trick.
If you mark everything before you start, work carefully, and your self-made marks are in the same place when you've finished, then the angular relationship
shouldn't change. But there are still ways it might; slight variations in belt tension, manufacturing tolerances, some have suggested that pattern parts, especially water pump pulleys, may not be dimensionally identical.
The 'official' method of fitting highly accurate setting tools and loosening the cam pulley is likely designed to ensure the precise angular relationship is maintained in spite of any differences in replacement part tolerances. This can get you a more accurate alignment than using timing marks. With the latter, you can only position a belt to the nearest tooth; if you loosen the cam pulley, you can position it anywhere.
Remember also that if it is not the first belt change since the car left the factory, there is no way of knowing what method was used during its previous replacement, and you can't be sure that the old belt is aligned with perfect accuracy.
My own opinion is that this is an unneccessary complication on what is basically a simple, low power engine; if Fiat had used fixed timing marks and keyed pulleys, it would only be at most half a tooth from the theoretically perfect position, and it would work just fine with that. But that's not how they designed and made it; we have to work with what we've got.