The admirable bishop emeritus of Richbourough, Mgr Edwin Barnes, in his admirable blog Antique Richborough, has raised the question of how 'traditional' receiving in the mouth is.
The short answer is in Jungmann Volume 2 pp374 ff; summarised thus: "the method dates substantially from the ninth century".
More than a millennium is quite a long time ... and I might add a point made by Dom Gregory Dix, when he was dealing with Reservation in a Tabernacle on or behind an Altar: that a common custom which has grown up separately in both the East and the West has a lot to be said for it. This also applies to the feeling that it is safer to put the Sacred Species into the mouth of the recipient. I say 'safer' because I get the impression from Jungmann that fear of the Host being taken away, rather than 'reverence', has a lot to do with the evolution of both the Western and Eastern customs.
[That is explicitly why Cranmer, in his 1549 Prayer Book, ordered the retention of Communion directly into the mouth (I suspect that, in 1552, the Communion Service was so desacralised that such apprehensions lost their force).]
This is still a reasonable apprehension. Perhaps not so very much in an ordinary stable congregation of decent devout people, but in some other circumstances. At Lancing, at Confirmations, one had to be constantly on the look-out for people from the extended families of the confirmati trying to take the Host away as a memento of the occasion. I remember once having to follow a recalcitrant woman down the church, insisting that she either consume or return the Host. I have heard of 'albums' from Weddings and Confirmations with Hosts neatly preserved behind sellophane! And the scrimmage that happens at big out-door papal Masses ... I watched the Fatima ceremonies on Vatican TV Player ... well, the less said about all that the better.
As we of the Patrimony might put it, "The Sacrament of the Lord's Supper was not by Christ's ordinance to be included in collections of souvenirs, but to be received with Faith".
So what about 'reverence'? I agree with Mgr Edwin about the complete decency of the traditional Anglican practice ...
... did I say 'traditional'? That's not really quite right. Pre-Tractarian prints make clear that earlier Anglican practice was to take the cube of leavened Bread from the Minister with the fingers. The more modern way represents an originally Anglo-Catholic appropriation of the practice described by S Cyril of Jerusalem in his Catecheses Mysticae (but shorn of the fancy bits about touching your eyes with the Host before consuming It). The custom spread, like so many things, from Tractarian practice to being the normal C of E custom.
Accordingly, Anglicans have commonly come up to the Communion Rails, knelt down, and received the Host onto the right hand which is supported by the left hand as by a throne, and received by lifting the palm of the hand to their mouths, and then checked, as S Cyril insists, that no crumb remained ("be careful that no particles fall, for what you lose would be to you as if you had lost some of your members. Tell me, if anybody had given you gold dust, would you not hold fast to it with all care, and watch lest some of it fall and be lost to you? Must you not then be even more careful with what is more precious than gold and diamonds, so that no particles are lost?").
That culture just has to be judged reverent, seemly, and decent. There, I agree with Bishop Edwin 100%.
However, to be completely frank and entirely personal: I find the 'mainstream' English Catholic practice quite upsetting. I am well aware that it is not for me to judge others, to whose devout interior dispositions I have no direct access. But the practice of approaching Holy Communion, making no act of reverence, receiving It onto the hand and then strolling away, meanwhile nonchalantly transferring the Host to the mouth, seems to my subjective Anglican eyes totally, and grossly, irreverent.