In this section, Pope Pius XII reminds bishops that the desire of the faithful to receive from the bread consecrated at the Mass in which they “attend.”
118. But the desire of Mother Church does not stop here. For since by feasting upon the bread of angels we can by a “sacramental” communion, as we have already said, also become partakers of the sacrifice, she repeats the invitation to all her children individually, “Take and eat. . . Do this in memory of Me”[1 Cor. 11:24] so that “we may continually experience within us the fruit of our redemption”[Roman Missal, Collect for Feast of Corpus Christi] in a more efficacious manner. For this reason the Council of Trent, reechoing, as it were, the invitation of Christ and His immaculate Spouse, has earnestly exhorted “the faithful when they attend Mass to communicate not only by a spiritual communion but also by a sacramental one, so that they may obtain more abundant fruit from this most holy sacrifice.”[Sess. 22, c. 6] Moreover, our predecessor of immortal memory, Benedict XIV, wishing to emphasize and throw fuller light upon the truth that the faithful by receiving the Holy Eucharist become partakers of the divine sacrifice itself, praises the devotion of those who, when attending Mass, not only elicit a desire to receive holy communion but also want to be nourished by hosts consecrated during the Mass, even though, as he himself states, they really and truly take part in the sacrifice should they receive a host which has been duly consecrated at a previous Mass. He writes as follows: “And although in addition to those to whom the celebrant gives a portion of the Victim he himself has offered in the Mass, they also participate in the same sacrifice to whom a priest distributes the Blessed Sacrament that has been reserved; however, the Church has not for this reason ever forbidden, nor does she now forbid, a celebrant to satisfy the piety and just request of those who, when present at Mass, want to become partakers of the same sacrifice, because they likewise offer it after their own manner, nay more, she approves of it and desires that it should not be omitted and would reprehend those priests through whose fault and negligence this participation would be denied to the faithful.”[Encyclical Letter Certiores effecti, par. 3]
There is a nod to practicality, of course: Communion from the tabernacle is also “taking part” in the Mass. But the language in favor of Communion from what is consecrated at the Mass seems fairly strong to me. What about to you?
Mediator Dei on the Vatican web site.
Catholic Sensibility 
Remember that, for centuries until Pius X, the average PIP probably received Holy Communion once or twice a year (Easter and perhaps Christmas) and in many areas very typically as they exited a confessional, not within the Mass properly speaking. Clerics, religious, and more elite laity who had access to regular spiritual direction and confessors (particularly royal and noble families with their own beneficed chaplains) might receive more frequently.