Except in cases of absolute necessity, a priest should always have a server. If this is not possible, Canon (liturgical) Law also allows a woman to make the responses (and even ring the bell), but from outside the Communion rail.
The Church insists on this point, as every Mass is actually a public and social act of the Mystical Body of Christ, particularly of Church Militant.
In fact, it used to be prohibited to offer Mass without a server unless the priest had a special papal indult; Fr. Charles Foucauld had to wait 3 years to get one, because he was in the middle of the Sarah desert and no server was ever avaialble.
Hence, in the case of the rubrics of the 1962 missal, it would be a defect for a priest to offer Mass without a server, if the situation did not warrant it.