Actually, your line of thinking doesn’t necessarily match what the Prefect for the Congregation for Divine Worship and the Discipline of the Sacraments has to say:
Well, the question of Eucharistic minister – you mean the Extraordinary Minister of Holy Communion, that is, those who will help the priest and the deacon when the priest and the deacon are not [sufficient] to give Holy Communion to the hundreds and hundreds and hundreds who are receiving Communion. That’s what we mean by Extraordinary Minister of Holy Communion. Which means that if the priests and deacons are many and sufficient for those receiving Holy Communion, nobody else should dare to come near the altar and touch the sacred vessel to distribute Communion, because they were not ordained for that.
It’s very important to stress that, because some people do not understand the whole point of these Extraordinary Ministers of Holy Communion. Some people think that it is a power struggle for lay people to prove that what the priest can do, so can they. Which means if there are not many people to receive Communion – suppose there are three priests or two priests and one deacon and 100 people to receive Communion – then there is no need for even one single Extraordinary Minister of Holy Communion.
Furthermore, this is what Redemptionis Sacramentum has to say:
It is the Priest celebrant’s responsibility to minister Communion, perhaps assisted by other Priests or Deacons; and he should not resume the Mass until after the Communion of the faithful is concluded. Only when there is a necessity may extraordinary ministers assist the Priest celebrant in accordance with the norm of law.173
…[157.] If*** there is usually present a sufficient number of sacred ministers for the distribution of Holy Communion, extraordinary ministers of Holy Communion may not be appointed. Indeed, in such circumstances, those who may have already been appointed to this ministry should not exercise it.*** The practice of those Priests is reprobated who, even though present at the celebration, abstain from distributing Communion and hand this function over to laypersons.258
[158.] Indeed, the extraordinary minister of Holy Communion may administer Communion only when the Priest and Deacon are lacking, when the Priest is prevented by weakness or advanced age or some other genuine reason, or when the number of faithful coming to Communion is so great that the very celebration of Mass would be unduly prolonged.259 This, however, is to be understood in such a way that a brief prolongation, considering the circumstances and culture of the place, is not at all a sufficient reason.
Therefore, it has nothing to do with a priest’s workload because he is the ordinary minister of Holy Communion. And, I wouldn’t even call it “workload”, since his first and foremost responsibility as a priest is to celebrate the Holy Sacrifice of the Mass. That is the end all and be all of his ministry.