It seems that villagers can't give their own bread to their friends. In the past, I have tried making a few infinite bread farms powered by villagers but they never seem to give away their bread. Even if the conditions are met, the villagers with bread only seem to rarely pass bread around, and that only happens if they have claimed a bed. Other crops can be farmed infinitely, so what happened to wheat?
EDIT: This has been happening since villagers swapped from their old AI to their modern AI.
EDIT: The real problem has been discovered! They need a bed.