Many churches do offer both the host and the chalice, but–they do not HAVE to do so.
Jesus offered the bread and the wine at the Last Supper FOR THE FIRST TIME. AT that first time, even though He had not yet died on the cross, the bread because not just His Body ALONE, and the wine His Blood ALONE, but each became Body AND Blood, Soul AND Divinity–BEFORE the actual bloody sacrifice on Calvary.
At the consecration, we do EXACTLY as Jesus did, when the priest consecrates the bread and wine–and, once again, now and forever, they become, EACH, Body and Blood, Soul and Divinity.
Because of people over the centuries becoming CONFUSED, and making the same honest mistake you appear to be doing, that somehow you have to have BOTH together, as if by taking ONLY the host or ONLY the cup, you are only getting, forgive the term, “HALF OF GOD”, the Church formally defined the ALREADY GIVEN DOCTRINE that BOTH host and chalice contain the TOTAL God–Body and Blood, Soul and Divinity.
Now, IF you live in a diocese, like most, which offers the chalice and host, not because “TWO GODS ARE BETTER THAN ONE”, but because they wish to allow for choice (there are many with celiac sprue who cannot take the host, but can take the cup, and many with cirrhosis, for example, who can take the host but NOT the cup) in order to allow as many as possible to receive ONE OR THE OTHER, that is fine. And there are those who receive Body and Blood not thinking that they are getting “more” but who do so in a spirit of piety and love, just rejoicing in being able to receive Christ.
I have to say that I honestly hope that one thing that changes in the U.S. IS the “both species” proliferation. . .entirely because of the attitude of those who inaccurately and unfairly conclude that unless they get “both” they just are getting only “half a loaf”. . .and that is totally wrong.
It is rather a pity that because there are so many who cling like death to their childish “we want it all” error, they spoil it for the rest who DO understand just what communion is all about.