It is ironic that the Roman Church successfully suppressed just about all the Rites which once flourished in the West in the early days but for the past few hundred years they have been hard at work filching the Byzantine Rites of the East!!! I wonder why don't they make similar efforts to restore their proper ancient Rites to the Irish and the Spanish and the French, etc? If Greek Catholics and Ukrainian Catholics may keep the Byzantine Rites, why cannot Irish Catholics and Spanish Catholics be allowed their own Rites?
If we look at the geographical territory of the Roman Patriarchate we find wide-spread suppression of local Rites over the centuries.
The wonderful Mozarabic Rite of Spain and Portugal was completely suppressed and allowed to remain, as a kind of museum piece, only in Toldeo, while the rest of Spain was required to adopt the Roman Rite. This was accomplished by Pope Alexander II (1061-1073) and later by St. Gregory VII (1073-1085). Today the Mozarabic Mass is celebrated once daily at the Capilla Muzarabe in the Toledo cathedral.
The Gallic Rites spread across France and Germany but were suppressed by the Papacy and by the Franks. By the end of the 9th century nothing remained and all had been replaced by the Roman Rite.
The Celtic Rites of Ireland, Scotland, Wales were entirely and utterly destroyed by the close of the 12th century. In Ireland this was accomplished at the insistence of the Papal Legate of Pope Adrian (at the Synod of Cashel in 1172AD) and with the assistance of the invading Anglo-Norman army.
So we see that some of the most sizeable areas of the Church of Rome--Spain, France, Germany, the Celtic areas--were obliged to abandon and suppress their ancient Rites and adopt the Rite of the Church of Rome.
(As an aside, the Celtic Rite, specifically the 8th century Irish Lorrha-Stowe Missal now has a small, very very small, revival in the Orthodox Church. It has been resurrected, and re-rubricised into a workable
Liturgy by Hieromonk of the Australian ROCA Diocese and awaits an episcopal blesing for its use. Whether it will ever be more than something for occasional use by liturgical enthusiasts is another question.)