It must be pointed out that Vatican II did not call for Communion under both species at all Masses but only at special occasions:
The dogmatic principles which were laid down by the Council of Trent remaining intact, communion under both kinds may be granted when the bishops think fit, not only to clerics and religious, but also to the laity, in cases to be determined by the Apostolic See, as, for instance, to the newly ordained in the Mass of their sacred ordination, to the newly professed in the Mass of their religious profession, and to the newly baptized in the Mass which follows their baptism.There is no theological objections, per se, against Communion under both species but there are serious practical problems, especially at large Masses, that cannot be lightly dismissed. Additionally, there has grown a school of thought requiring Communion under both species that has serious theological problems which I have pointed out above. The emphasis on the manner of reception rather than on the WHO of reception weakens our faith in the reality of the Eucharist. The entirety of the Body and Blood of Jesus Christ is present under the smallest particle of either species. The insistence on Communion under both species as the only valid way to receive attacks this truth.
Sacrosanctum Concilium, no. 55.
Many of the practical problems with Communion under both species could be resolved if we were to seriously consider the use of intinction. Many, however, object because:
1) it differs from the manner in which the priest receives,
2) it precludes Communion in the hand, and
3) it goes contrary to what is an overemphasis on the act of drinking which clouds the reality of the person who is received, Jesus Christ.
As a chalice bearer in my Anglican (not episcopalian) parish I have noticed that over the years more and more people are dipping rather than sipping. I know a lot will cite germ concerns, but the fact is that germs are more of a problem with dipping rather than sipping. Of course, considering that the question concerns the Blood of Christ, germs wouldn’t be a problem anyway.
As you may be aware, the Anglican Church did away with Communion in One Kind in 1559 (it was retained by Henry VIII, abolished by Edward VI, reinstated by Mary I, and ended by Elizabeth I). The reason is simple, we are commanded to eat the Flesh of the Son of Man and drink His Blood. He said we must do both. Everywhere one is mentioned, the other is also mentioned. Nowhere are they distributed to two different sets of people. Therefore, in light of Christ’s instruction (John 6) and His institution (Last Supper), the Flesh and Blood ar both part of the Sacrament and both should be distributed to all who are worthy to receive.