Only a priest can confect the Eucharist because the commission of Christ “do this in memory of me” was given to the apostles.
The apostles and their successors, the bishops, have the fullness of Holy Orders. Priests are close “co-workers” with bishops. In fact the Latin term sacerdos, that is, “priest,” includes both the orders of priest and bishop. The more specific term presbyterus refers specifically to priests (not bishops) while episcopus refers to bishops (not priests).
Thus, within the sacrament of Holy Orders, the priesthood is connected closely with the episcopacy. How? Both the priest and the bishop are configured to Christ the Head of the Church and are thus able to represent God before the people and the people before God.
Deacons, in contrast, are configured to Christ the servant. Thus, they assist at the altar but also with the “ministry of Charity.” In the New Testament, for instance, the apostles ordain deacons who are in charge of taking care of widows, the sick, etc. so that the apostles are free to carry out their primary duty of teaching, sanctifying, and governing.
St. Ignatius of Antioch (ca. A.D. 117) wrote (I believe to the Ephesians) that the only “valid Eucharist” was the one celebrated “by the bishop or by one delegated by him.”