It seems that every time this issue comes up, it turns into a rather cantakerous debate. I certainly do not want to offend anyone, clergy and laity alike.
This thread is also two years old.
It would seem to me that once the CDWDS issued its statement, it would have been taken for its merit by the proponents of this kind of blessing. But, unfortunately, that has not been the case, as post after post clearly indicates.
The diaconate plays an invaluable role in the Church. In fact, an important one, as the Apostles, themselves (see Acts) decreed that the assistance of the deacons was needed. However, just as the celebrant has a role to play in the Holy Sacrifice of the Mass, so, too, does the deacon and so, to, do the faithful. Now, if after preaching the deacon imparts a blessing, fine. He is doing that within the context of his duties as preacher. However, Ecclesia de Mysterio makes very clear that there are certain things that fall within the purview of the celebrant alone. Blessing individuals within the context of the Mass, though not explicitly mentioned, is implied when the document speaks of gestures and words that are reserved to the celebrant alone.
As far as the imparting of a blessing is concerned, the CDWDS, as Fr. David pointed out, makes perfectly clear that:
In a similar way, for others who are not to be admitted to Holy Communion in accord with the norm of law, the Church’s discipline has already made clear that they should not approach Holy Communion nor receive a blessing.
This is not being uncharitable. It is stating a fact. Furthermore, what would be uncharitable would be to continue to promote something (that has no liturgical Tradition behind it) and pass it off for something that it is not. It also serves to breed confusion as the genuine reason for the line starts to blur. We line up to receive Someone, Jesus, not something, a blessing, which will be given to all at the end of the Holy Sacrifice of the Mass.
If those who desire a blessing, whether for themselves or for their children, wish to have one, apart from the one that everyone receives at the end of Mass, there is nothing stopping them from approaching the deacon, priest or bishop at the end of Mass and requesting it. That would be the appropriate time, but, not during the distribution of Holy Communion.