"The bread and wine are arranged, divided, incensed; and many prayers are said over them involving the idea of an offertory. "
Wrong! There is nothing in the preparation of the bread and the wine which, at least the East, has ever been considered to be an offertory in the sense that we all use that term. The offertory is quite well defined within the Divine Liturgy of +John Chrysostoms. Frankly, the earliest writings, when they speak in any detail at all, always speak of the deacons or priests carrying the offerings in procession. I must say your quote from the Catholic Encyclopedia appears to me to be a post hoc propter hoc sort of spin to lend an air of ancient authority to a truly innovative practice. By the way, where did the lugging of a basket of money down with the bread and wine come from?
Personally, it makes no difference to me if in Latin Rite Churches lay people process up to the solea with the gifts. How the Latin Church conducts its liturgies, within certain parameters, is the business of the Latin Church. I do think its unfortunate to use that act to buttress a theological point, however.
I intentionally posted the source - the newadvent.org web site that purports to be the Catholic Encyclopedia. Recall the discussion we had several weeks ago where the web master of this site had posted outdated information about St. Maron (couldn't even spell his name) so I will discount it. However, I would be most interested in any link to the early Church Fathers that explains how the offertory was handled in those first centuries. As I recall from the pre VCII days, the priest carried the offerings with him when he processed during the Entrance dialogue, but I am no longer sure.
The quoted Encyclopedia dates from fifty years before the offertory procession was begun, or re-established, or whatever.