In light of the fact that Donatism is heresy, why do most churches require a priest to bless the elements?

I read this question a while ago and even though it has a satisfactory answer, I thought that there would be something more accessible in The Lamb's Supper by Dr. Scott Hahn. And I think these tidbits will help.

He says that thoughout the Church (and throughout the ages) there many Eucharistic prays but they all contain the same parts. The Epiclesis (when the priest places his hands over the bread and wine calls down the Holy Spirit) and the The Narrative of Institution (when the bread and wine is transformed into Christ's Body and Blood) are the foremost of these parts.

The priest relates the drama of the Last Supper, when Jesus made provision for the renewal of His covenant sacrifice through all time.

...

When the priest speaks the words of institution-"This is My body ... This is the cup of My blood, the blood of the new and everlasting covenant'-he is not merely narrating, he is speaking in the person of Christ, Who is the principal celebrant of the Mass. By the sacrament of Holy Orders, a man is changed in his very being; as priest, he becomes "another Christ." Jesus ordained the Apostles and their successors to celebrate the Mass when He said: "Do this ... in remembrance of Me" (1 Cor 11:25). Note that Jesus commanded them to "do this" and not "write this" or "read this".

That last sentence summarizes why regular folks can't do it because we'd just be reading the words and they'd have no effect. The understanding of scripture as handed down by the Sacred Traditions of the Catholic Church in the Sacrament of Holy Orders have apparently chosen to interpret the person Jesus is commanding to "Do this" as not me and my wife at dinner, but the people He was actually talking to and those who were appointed by the people He was talking to take their place.

As a youth leader I celebrated the Lords Supper with my students with no ordained minister present—and all the ministers of my church knew. Baptists can celebrate communion at home with the family. The early church did the same: after the meal, the bread was taken and broken remembering Jesus' sacrifice.

If a pastor is present, we do respect his position and allow him to preside, much like in the Anglican church where a priest defers to a bishop if one is present. I have never heard of a Baptist church which teaches that communion is invalid if a pastor is not present. My church even allowed me to baptize my son.

Baptists believe strongly in the "priesthood of all believers". The temple worship is done away with; our High Priest is Jesus Christ, and all believers are are priests on earth (according to Baptist belief).

I would also point out, that even under the old covenant, no priest was required in order to celebrate the Passover in the home. The High Priest did offer the paschal lamb in the temple; but since Christ, our High Priest and our paschal lamb, has already been sacrificed, no further sacrifice is needed. So Baptists believe the Lords Supper is a memorial meal, not a sacrifice—it is Holy and real, connecting us to Christ and to each other through the Holy Spirit.

As far as the Roman Catholic Church and the Church of England are concerned, it certainly is Canon Law.

900 §1. The minister who is able to confect the sacrament of the Eucharist in the person of Christ is a validly ordained priest alone.

907 In the eucharistic celebration deacons and lay persons are not permitted to offer prayers, especially the eucharistic prayer, or to perform actions which are proper to the celebrating priest.

[CLC]

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B 12 Of the ministry of the Holy Communion

1. No person shall consecrate and administer the holy sacrament of the Lord's Supper unless he shall have been ordained priest by episcopal ordination in accordance with the provisions of Canon C 1.

[Canons of the Church of England]

That the Eucharist is not affected by the worthiness of the minister is also enshrined in a number of church documents (Article 26 in the Church of England, for example).

However, an unworthy minister is still a minister. The ontological change wrought by the Spirit at ordination is what makes a man able to effect the sacrament. Whether he is worthy or not is of no consequence. A layman has not undergone that ontological change, and so is unable to celebrate the Eucharist. He can say the words and do all the right actions, but it is simply not effective.

The Catechism of the Catholic Church addresses this:

1141 The celebrating assembly is the community of the baptized who, "by regeneration and the anointing of the Holy Spirit, are consecrated to be a spiritual house and a holy priesthood, that . . . they may offer spiritual sacrifices."⁹ This "common priesthood" is that of Christ the sole priest, in which all his members participate:¹⁰

Mother Church earnestly desires that all the faithful should be led to that full, conscious, and active participation in liturgical celebrations which is demanded by the very nature of the liturgy, and to which the Christian people, "a chosen race, a royal priesthood, a holy nation, a redeemed people," have a right and an obligation by reason of their Baptism.¹¹

1142 But "the members do not all have the same function."¹² Certain members are called by God, in and through the Church, to a special service of the community. These servants are chosen and consecrated by the sacrament of Holy Orders, by which the Holy Spirit enables them to act in the person of Christ the head, for the service of all the members of the Church.¹³ The ordained minister is, as it were, an "icon" of Christ the priest. Since it is in the Eucharist that the sacrament of the Church is made fully visible, it is in his presiding at the Eucharist that the bishop's ministry is most evident, as well as, in communion with him, the ministry of priests and deacons.

9 Lumen Gentium 10; cf. ⇒ 1 Pet 2:4-5.
10 Cf. LG 10; 34; Presbyteriorum ordinis 2.
11 Sacrosanctum Consilium 14; Cf. ⇒ 1 Pet 2:9; ⇒ 2:4-5.
12 ⇒ Rom 12:4.
13 Cf. PO 2; 15.