If the procession into church were a sentence, then the cross is the subject.
I attended a local parish where, oddly, a closet had been built behind and slightly to the left of the altar where Mass is celebrated.
Well…the procession into church was OK but the little guy carrying the cross marched right up and put the cross IN THE CLOSET. This was the protocol for procession in and out of church.
If I were a priest, the processional cross would be installed directly in front of the altar, and I’d stand there in front of it, for all 17 verses of the entrance hymn. Obviously, I don’t have a utilitarian view of music, just to get the priest from point A to point B. The entrance hymn should be the rousing hymn of praise and the focus should be on the cross, at least for that time, IMHO.