I’ve seen a lot, but I’ve not heard of this before.
As others have said, your son is an Eagle and the ECOH is not part of the advancement process, which has been completed. The Troop, District, and Council have completed their official part in the process.
From here forward, it’s personal. Yes, even the BSA says there should be a celebration and recognition, but that’s just a traditionally recognized formality, kind of like taking off the or putting the hand over the heart during the National Anthem. Nobody is obligated to give your family a ECOH. But, I’ve never heard of an Eagle b