When the pilot bearing goes, the preload on the other bearings is no longer what it should be. Things are no longer locked in place.
Note that the sleeve in this picture seats against the back of the pilot bearing:
If the pilot bearing goes bad, I believe it introduces looseness, or another way of saying it: the bearing allows longitudinal movement after it is damaged. That longitudinal movement causes the rest of the stack of components on the pinion shaft to no longer be locked in place. Think of it this way: the pinion gear/shaft is engaging with the crown gear, which resists rotation because of tires on the ground. I think that when the stack of parts bearings and spacers become no longer "locked" in place because of the looseness introduced by the bad pilot bearing, the pinion gear can literally pull itself closer toward the crown gear.
When everything is locked in place with tight bearings and correct torque on the pinion nut, the pinion gear is locked in position. It can't move forward or backward longitudinally. When the pilot bearing fails, the the pilot bearing inner race which is up against the sleeve in the picture above is no longer locked in place. It can shift longitudinally. This introduces looseness in the rest of the stack of components on the pinion gear.
Then the pinion gear, acting on the crown gear, because of the way it is cut, literally pulls itself toward the crown gear due to the force coming from the engine/driveline. The looseness in the "stack" allows the pinion/shaft to pull itself - to slide within the front and rear pinion bearings (these are only a press fit). After the pinion gear/shaft has moved, then the pinion to crown gear relationship has gone all to hell vs. what it should be. And lots of noise ensues.
Anyway, that is my attempt to describe what I think can happen.
I am hopeful that replacing the pinion bearing and setting preload properly is all you will have to do to fix your issue.