I’m going to offer a slightly different perspective from a priest than that of my confrere. While I respect Fr. David’s position, and he’s right that priest are obligated to celebrate the liturgy according to what is laid out in the Roman Missal, my take on this is two-fold.
First, I don’t refer to it as a “blessing,” per se, except perhaps colloquially. Rather, what I call it is “an invitation to a spiritual communion,” and when someone comes to me in the communion line who cannot receive Holy Communion, I simply say, “Receive the Lord Jesus in your heart.” It’s not a blessing. It’s receiving communion, but rather than receiving the Eucharist, it’s a spiritual communion.
Second, and this is really my bigger point…at weddings and funerals there are many (often even most) who cannot receive the Eucharist, either because they are not Catholic or because they are not in a state of grace. So, prior to distribution of Holy Communion at these liturgies, I say something along the lines of, “For anyone who is not Catholic or who is not prepared to receive Holy Communion today for whatever reason, please feel free to either remain in your pew or to come forward with your arms crossed over your chest as a sign that you would like to receive a blessing (and I do say “blessing,”…again, colloquially).” This seems to me a far better alternative than A) excluding someone at a wedding or funeral for a loved one when I don’t have time to do an adequate catechesis as to why that person is seemingly excluded, or B) inviting people to make sacrilegious communions. Let’s be honest…most people are not going to hang back in their pew, especially when they are accustomed to coming forward each week, essentially saying, “Hey! Look at me! I’m in a state of serious sin!!!”
Offering this as an option prevents countless sacrilegious communions, and as such, I think is far better for the person’s soul, and potentially my soul as well.