Communion in one kind is not automatically a “trivialization” (as a Protestant critic charged). The fact remains that given the assumption of bodily Real Presence, Jesus is fully present under either form (since He can’t be divided). This is a biblical teaching:
1 Corinthians 11:27 (RSV, as throughout) Whoever, therefore, eats the bread or drinks the cup of the Lord in an unworthy manner will be guilty of profaning the body and blood of the Lord.
Note the all-important “or.” This shows that Jesus is fully present in either. If we profane the consecrated host, we are guilty of the body and blood of Christ. The logic (even the grammatical structure or syntax) is unassailable. Jesus Himself also alludes to one form only being salvific:
John 6:33-35 For the bread of God is that which comes down from heaven, and gives life to the world.”  They said to him, “Lord, give us this bread always.”  Jesus said to them, “I am the bread of life; he who comes to me shall not hunger, and he who believes in me shall never thirst.
John 6:50-51 This is the bread which comes down from heaven, that a man may eat of it and not die.  I am the living bread which came down from heaven; if any one eats of this bread, he will live for ever; and the bread which I shall give for the life of the world is my flesh.
John 6:57-58 As the living Father sent me, and I live because of the Father, so he who eats me will live because of me.  This is the bread which came down from heaven, not such as the fathers ate and died; he who eats this bread will live for ever.
These passages don’t exclude both forms, but they do show that one only is quite sufficient for the purpose of receiving our Lord Body, Blood, Soul, and Divinity: a thing directly tied to salvation (John 6). The widespread withdrawal of the cup had nothing to do with a goal of deliberate deprivation, and everything to do with hygienic and reverential considerations. It was much easier for abuse to take place with liquid. It was also more difficult and risk-laden to take the Eucharist to the sick in their homes (as was widely done in the early Church) in liquid form.When many Protestants later ceased believing in the Real Substantial Presence altogether, such considerations were irrelevant: a little wine (or the unbiblical grape juice, due to the social pressure of the temperance movement) splashes out? So what: it’s only symbolic, anyway. No biggie. But when one believes that it is literally our Lord Jesus, then the utmost care is taken.
Moreover, how sacraments or liturgy are conducted in details is a relevant consideration as well. I could just as well argue that the Calvinist tradition trivialized baptism by not routinely using immersion, which seems indicated or some kind of norm, at least in some Bible passages. It was deemed a proper development and not fatal to the essence of baptism, by most Protestants, to allow pouring or even sprinkling. The Baptist would argue, on the other hand, that immersion as well as adult baptism are both central or essential to the rite and sacrament. Most Christians (including the majority of Protestants) disagree.
Lastly, those of us who believe in baptismal regeneration (the vast majority of all Christians throughout history) also hold that to deny that result is to violate the very essence of the sacrament: to “gut it” of its power and central purpose. But these are the same kinds of arguments made with regard to Holy Communion: because Rome didn’t allow the cup for many years, somehow it was “trivializing” the sacrament. It simply doesn’t follow; and the more one understands the reasoning, the less force this objection has.
The only case that has any “teeth” at all here is the complaint about infrequent communion. But the Church in due course changed that. I’m not sure what the earlier rationale was.