In summary, if you consume the host, then (not being a requirement after consuming one or the other), then the only purpose for partaking in the chalice is I guess for a feeling of completeness? … good measure?
I used to receive under both species regularly, but I realize that, in the United States at least, the constant concession of the Chalice to the laity creates an environment where extraordinary ministers of Holy Communion are
constantly used. I am not a supporter of this overuse and misuse of an
extraordinary ministry, and
I have documented the “explosion” of the circumstances where the Chalice may be offered to the laity.
In the words of the Church (
Eucharisticum Mysterium 32, from 1967):
Holy communion has
a more complete form as a sign when it is received under both kinds. For in this manner of reception (
without prejudice to the principles laid down by the Council of Trent, that under each element Christ whole and entire and the true sacrament are received), a fuller light shines on
the sign of the eucharistic banquet. Moreover there is a
clearer expression of that will by which the new and everlasting
covenant is ratified in the blood of the Lord and of the relationship of the
eucharistic banquet to the eschatological banquet in the Father’s kingdom (see Mt 26:27-29).
I do not have a personal need to receive under both kinds in order to (better) recognize the sign of the Eucharist, nor that the New Covenant was ratified in Christ’s blood, nor that the Eucharist we partake of on earth is a foreshadowing of the eschatalogical marriage supper of the Lamb in Heaven, where the sacramental veil will be lifted, and we will see God face to face as He is.
As such, I now only receive under both kinds on particular occasions, such as the Solemnity of the Most Holy Body and Blood of Our Lord.
(P.S. If you have been to the Liturgy of the Passion on Good Friday, you will notice that it is
not a Mass but a Communion service: the priest does not pray the Eucharistic Prayer, and (formerly consecrated and reserved) Holy Communion is distributed under the form of bread only.)