Catholic ordinations always take place in a Mass, and the presider is always a bishop. The bishop presides over any liturgy, priests only act as his representative with his mandate (cf. e.g. Lumen Gentium 26). In the ordination liturgy itself, the newly ordained priests assist the bishop as concelebrants (a quite unfortunate term in my eyes, but be that as it may) for the rest of the Mass. So far, so good.
But then there is the tradition of the “first blessing” of a newly ordained priest where it starts to get a bit complicated. How does the first blessing relate to the ordination liturgy itself? The Latin Pontificale leaves no doubt: There is no first blessing whatsoever in the ordination Mass. The presiding bishop gives the final blessing of the Mass, and after the dismissal the Mass is over. Anything else can take place afterwards following local custom.
The English Pontifical follows the Latin, but I am familiar with a well-known custom that the bishop asks the newly ordained priest(s) to bless him before the dismissal. He kneels down in front of the priest(s) and receives the first blessing.
The German Pontifikale allows including the first blessing in an odd way: Where it is custom, the newly ordained priests can give the first blessing together before the final blessing of the Mass by the bishop. (“Wo es Brauch ist, können die Neupriester vor dem Schlusssegen des Bischofs gemeinsam den Primizsegen erteilen.”)
I have even been in ordination Masses where only the newly ordained priests gave the first blessing without any final blessing by the bishop, but this practice is not foreseen by the Pontifikale.
None of these options make sense to me, with the German option of a double blessing probably being the most irritating. When I studied medieval church history with the well-known professor Arnold Angenendt, I learned the early medieval concept of “pure hands” or “powerful hands”: The hands of a newly ordained priest have fresh and unspent power, hence people – even bishops – should crave such a pure blessing and literally go any distance to get one.
But from the point of view of ecclesiology, liturgical symbolism, and the theology of the ordained office after Vatican II, this notion is not convincing.
In general, the symbolism of a bishop being blessed by a non-bishop can make good sense. Acts 13:1–3, where the Christians in Antioch laid their hands on Barnabas and Saul before they sent them to Seleucia and Cyprus, might be a good example and analogy. Blessing is not a one-way road among Christians. The biblical meaning of a blessing is not only someone “with power” acting over someone “without power,” but also praying to God for someone. Any Christian should be willing to bless anyone, and even bishops (maybe bishops more than others!) should crave being blessed. We also know liturgical reflections of that idea, e.g., there were times when the pope received Holy Communion from the hands of a deacon (and never took it on his own), or when the presider’s assistants prayed for him in the Penitential Act in the same way he prayed for them. (I think we lost a lot when we lost those two traditions.)
But this is not the point in the context of current liturgical symbolism. Priests bless bishops in a public liturgical act only in this one case. It is not part of a general liturgical rule of “bishops being blessed”. It is not covered by the Latin Pontificale, and it matches neither Lumen Gentium 26 nor Sacrosanctum Concilium 13 with their clear distinction between sacred liturgy and popular devotion. The symbolism of the presiding bishop as an image of the apostolic roots of the Church and of the unity of the Church – with the priests as his helping hands and not the other way round – is quite clear and should not be called into question by any (medieval) custom of popular devotion.
So when I attend the next ordination Mass, I would be most happy if I could receive the final blessing by the presider, and if I could decide on my own whether I ask for a first blessing by a newly ordained priest or not.