Well, the accounts of the council obviously intend to depict a situation where they recited the entire canon. However the canons they depict are those of the different schools. The Pali, for example, starts with the Brahmajala and Samannaphala suttas, because they begin the sutta collection in Pali. The Sarvastivada version begins (rather more reasonably) with the Dhammacakka and the Samyutta.
We know from independent grounds, however, that the canons as they are today cannot have existed in their entirety at that time. Even the commentaries acknowledge that certain suttas and passages were added later. So the claims of the schools should not be taken on their face value as a literal assertion, but rather, that the community gathered to recite the canonical collections that we know today as the EBTs.
DN 29:
I have today disciples who are competent senior monks, middle monks, junior monks, senior nuns, middle nuns, junior nuns, celibate laymen, laymen enjoying sensual pleasures, celibate laywomen, and laywomen enjoying sensual pleasures. Today my spiritual life is successful and prosperous, extensive, popular, widespread, and well proclaimed wherever there are gods and humans.
Of all the teachers in the world today, Cunda, I don’t see even a single one who has reached the peak of material possessions and fame like me. Of all the spiritual communities and groups in the world today, Cunda, I don’t see even a single one who has reached the pinnacle of material possessions and fame like the mendicant Saṅgha. And if there’s any spiritual path of which it may be rightly said that it’s endowed with all good qualities, complete in all good qualities, neither too little nor too much, well explained, whole, full, and well propounded, it’s of this spiritual path that this should be said.
Uddaka, son of Rāma, used to say: ‘Seeing, one does not see.’ But seeing what does one not see? You can see the blade of a well-sharpened razor, but not the edge. Thus it is said: ‘Seeing, one does not see.’ But that saying of Uddaka’s is low, crude, ordinary, ignoble, and pointless, as it’s only concerning a razor. If there’s anything of which it may be rightly said: ‘Seeing, one does not see,’ it’s of this that it should be said. Seeing what does one not see? One sees this: a spiritual path endowed with all good qualities, complete in all good qualities, neither too little nor too much, well explained, whole, full, and well propounded. One does not see this: anything that, were it to be removed, would make it purer. One does not see this: anything that, were it to be added, would make it more complete. Thus it is rightly said: ‘Seeing, one does not see.’
6. Teachings Should be Recited in Concert
So, Cunda, you should all come together and recite in concert, without disputing, those things I have taught you from my direct knowledge, comparing meaning with meaning and phrasing with phrasing, so that this spiritual path may last for a long time. That would be for the welfare and happiness of the people, for the benefit, welfare, and happiness of gods and humans. And what are those things I have taught from my direct knowledge? They are the four kinds of mindfulness meditation, the four right efforts, the four bases of psychic power, the five faculties, the five powers, the seven awakening factors, and the noble eightfold path. These are the things I have taught from my own direct knowledge.