Breeding animals takes many generations to get desired traits, so all this information would help to identify a problematic lineage. Since these pigeons were used to deliver critical messages if you had a lineage who began to lose their homing abilities it could be very costly.
Imagine a small group of scout soldiers whom find an unknown opposition encampment. They need additional forces to get there quickly or they may lose the chance to weaken those forces. If the pigeon is less likely to return home, they likely wouldn’t want to leverage them for these critical missions.
Having a clear and traceable record makes it so they can selectively breed the best pigeons and/or assign the best pigeons to the right tasks. Without clear and consistent records like these it would be akin to pissing into the wind and hoping you don’t get wet.