Actually, Quo primum was not designed to stop local customs. It expressly permits the continuation of local rites of a certain age, and indeed local rites did continue (and still do).
If you want to define centuries-old, Apostolic-origin rites as "local customs", then you're correct. But under the common understanding of "local custom", the Ambrosian, Byzantine (etc) rites were older than 200+ years at the time of 1571, so they were allowed to continue; they aren't local customs but true liturgies. The main reason being they were Apostolic/Church Father origin. All of the various local customs were gone after 1571, as they should've been.
.
In fact as late as the 19th century, in response to Guéranger and others, Pius IX, while admitting that the universal adoption of the Roman rite in France would be good, that it would cause more harm than good. Furthermore, the uniformity of liturgy in the twentieth century would indeed not be a restoration of tradition but decidedly contrary to the centuries of diverse liturgical practice.
I assume you're speaking of the Gallican rite, which is centuries and centuries old. You can't compare this rite to the many, many variations which existed in 1571.
.
One could defend the Dialogue Mass in the same way, as "a RESTORATION of past Tradition and he decreed it for the WHOLE church." This last part is not true, either. The liturgical reforms of Pius X only applied to the Roman rite and thus not even to the whole of the Latin Church and of course did not affect the various Eastern churches in union with Rome.
The point is, the Dialogue mass is not Traditional, nor Apostolic. The Gallican rite can trace its history back to the early Church. The Dialogue mass is a novelty; you can't "restore" something new.