There was a time, however, when the Mozarabic or Spanish Rite had its own particular Church, so did the Celtic rite and the Archbishop of Milan was head of that Church’s rite (in fact, liturgical scholars have discovered an interesting thing - in the ancient Milanese missals whenever the term “pope” is used, this actually refers to . . . the Archbishop of Milan!).
For Western groups who would like to come into union with Rome, there can be no doubt that, for them, the issue of “Rite” is not as nearly significant as the issue of their ability to govern themselves as particular Churches in union with Rome.
For example, there is the Anglo-Lutheran Catholic Church which is essentially a group of Lutherans who have already agreed with everything that the RC Church teaches and have applied to Rome to be accepted as a particular Church. Their plan is to create a church which is “culturally Lutheran” but which is Latin-Rite in all other areas (they practice German religious traditions, display the Rose of Luther etc.). In their parishes, one will see pictures of Pope Benedict and the like. They and their Metropolitan simply await the go ahead of Rome.
I am close to Anglicans who want to become part of the Ordinariates and they are already as Catholic as can be (they don’t see themselves as having anything to do with the Anglican/Episcopal communion whatever).
The Ordinariates base themselves on the “Anglican-Use” parishes in the U.S., but expect to bring in even more from their Anglican traditions, the full Book of Common Prayer in the Catholic recension, etc. They are also asking Rome to regularise their veneration for King Charles the Martyr, the Anglican King who was beheaded for defending a Catholic principle - that of Bishops in the Church. Many Anglican converts to Catholicism, including Bl. John Henry Newman and Ronald Knox, venerated King Charles I privately throughout their lives (there is a picture of King Charles in Newman’s private chapel, for example). The Anglican Catholics coming into union with Rome are not only “Catholic,” but are traditional in the sense that Tridentine Catholics are. Some of them are bitter about how their Anglican prelates have, in their view, mishandled the entire relationship with Rome to the point where their beloved church is in a shambles (as they tell me).
There are “liberal” Catholics up here who are actually very much against these traditionalist Anglican Catholics coming into union with Rome - they feel they will 'stack" the traditionalist opposition against them.
When the Ordinariates are in place, I think we will see an ever greater influx of Anglicans into union with Rome - Anglicans are, by nature, uncontroversial but, as in the case of one Anglican Catholic parish on the short list for membership in an Ordinariate, as soon as word of this got out, that parish now has many more members attending it from the mainstream Anglican church. They enjoy the beauty of their Anglican “whatever you wish to call it” and want traditional Christian moral principles to be reaffirmed.
All such roads appear to lead to Rome.