The Didache doesn’t spell out everything. It is a relatively brief document. In regards to the Eucharist, we have another very powerful witness to the necessity of a priest presiding in St. Ignatius of Antioch, a disciple of the Apostle John. Around the year 107 he wrote:
Chapter 7. Let us stand aloof from such heretics
They abstain from the Eucharist and from prayer, because they confess not the Eucharist to be the flesh of our Saviour Jesus Christ, which suffered for our sins, and which the Father, of His goodness, raised up again. Those, therefore, who speak against this gift of God, incur death in the midst of their disputes. But it were better for them to treat it with respect, that they also might rise again. It is fitting, therefore, that you should keep aloof from such persons, and not to speak of them either in private or in public, but to give heed to the prophets, and above all, to the Gospel, in which the passion [of Christ] has been revealed to us, and the resurrection has been fully proved. But avoid all divisions, as the beginning of evils.
Chapter 8. Let nothing be done without the bishop
See that you all follow the bishop, even as Jesus Christ does the Father, and the presbytery as you would the apostles; and reverence the deacons, as being the institution of God. Let no man do anything connected with the Church without the bishop. Let that be deemed a proper Eucharist, which is [administered] either by the bishop, or by one to whom he has entrusted it. Wherever the bishop shall appear, there let the multitude [of the people] also be; even as, wherever Jesus Christ is, there is the Catholic Church. It is not lawful without the bishop either to baptize or to celebrate a love-feast; but whatsoever he shall approve of, that is also pleasing to God, so that everything that is done may be secure and valid.