Posts 7, 8, 9, and 13 nail it, but I would additionally like to emphasize one item quoted in post #12, which frames the character of the Mass properly.
[to approach for an unauthorized blessing’] dilutes the sense of hunger for the Eucharist in those who cannot yet receive it.
Mass is not a secular social event. It’s a sacred, liturgical event, with “participation” (kind and level) specific to the proper role of each participant. Thus, priest participates in one way, lay attendees in quite another. Those in a state of grace, properly disposed, validly initiated, and observing the minimum fast, have the permission, encouragement, and assumption, of partaking of the Eucharist, those not meeting those criteria do not.
The communion line is reserved for those participating in the Eucharistic banquet. Parents virtually must bring babies in arms, who cannot generally be left alone in the pews. Sometimes the priest blesses such babies on the forehead, acknowledging their blessed presence
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Recently on EWTN radio, a priest was explaining the often-misunderstood word “participation,” in liturgical context. It doesn’t mean activity. It doesn’t mean “me,too.” It doesn’t mean joining the crowd. It means fulfilling the role appropriate to station, situation, and disposition. It means joining the mind and heart (and lips and voice, in prayer and song at designated times) with the priest who is God’s minister offering the sacrifice with us. (His role belongs to the ministerial priesthood; our role is of the priesthood of believers.)
Possibly the single most misinterpreted word of Vatican II was the word ‘participation.’ In its most egregious manifestation, it results in an illegitimate mandate for lay preaching in place of the priest’s homily – a flagrant usurpation of the priest’s role.
Reaffirming nevertheless that the Mass is not a secular social event, think about how silly it would be, in a buffet line at a reception – if you had no intention of eating – to simply walk through the line with a plate in your hand, collecting nothing, “just so that you wouldn’t feel left out.” By staying in your seat instead, you are participating in the reception nevertheless, without eating a morsel of food.
In the Mass, our reverent presence = participation. That would include the “hunger” for a meal we’re not ready to partake of. (Partaking is not equivalent to participation.)
That’s why the converse is also true: It is a serious sin to neglect Sunday attendance at Mass without sufficient excuse (such as illness), even when we are not prepared to receive the Eucharist. It is our participation (presence) that is important.
If the blessing was ‘better’ just because he’s holding Christ before you, he certainly wouldn’t be much of a priest outside Mass.