That, however, is more to do with worldly success than anything else. Spain, Portugal, France, and Britain colonised the world. They brought their local Catholicism with them, and it was Latin Catholicism. If Spain was Byzantine then I have no doubt that the Byzantine Rite would have flourished in Latin America.
Yes. That’s how I got my Catholicism: from Spain to the Philippines.
The key difference is in the ethnic composition of the churches, not the rites. Even during the age of colonization, the Latin church already had many ethnicities, and that was through missionary effort, not conquest. Ireland, England, France, Germany, etc. were all evangelized, not colonized and they were all part of the Latin church.
The Byzantine Rite was also carried from the Eastern Roman Empire to the Slavs, also through evangelization, which is why the Russians, Ukrainians, Bulgarians, Slovaks, etc. are Byzantine. But their churches are along ethnic lines, unlike the Latin church, which is multi-ethnic. You have the Russian Orthodox/Catholic church, Ukrainian Orthodox/Catholic church, etc, and the ethnicities are sharply defined.
An even more strict example is the Syro-Malabar Knanaya Catholic church, which is not only ethnic, but endogamous.
And that is where the confusion comes in. I believe the OP actually had churches in mind, rather than rites. And the set relationship between rites and churches differs in the East and the West.
In the East, the churches tend to use a particular rite, e.g. the Greek Catholic Church, the Ukrainian Greek Catholic Church, the Melkite Catholic Church, etc. use the Byzantine Rite.
In the West, we pretty have only one church, the Latin. Unlike in the East, the Latin church has multiple rites. The Roman Rite is of course the most prevalent, but the others (Ambrosian, Mozarabic, Bragan, Gallican, Carmelite, Dominican, etc.) are all Latin rites and part of the Latin church.
In the OP’s context, it’s clear he means that the Eastern churches are more ethnically defined than than the Latin church (not rites). People are members of churches, not rites.
“The Popes and the Roman Church have found Latin very suitable for many reasons. It fits a Church which is universal, a Church in which all peoples, languages and cultures should feel at home and no one is regarded as a stranger.”
What do you mean by that? The Roman Canon (starting with “Te igitur clementissime Pater”) was supposedly written in Latin and a Missal of, say 750 A.D., would be recognizeable (save for the fonts) to someone who attends either the Latin OF or EF. Why doesn’t it make sense? Latin had been the administrative language of the Roman Empire and Church documents, Scripture, etc. were preserved in Latin going forward, many by Greeks themselves. It only made sense the liturgy (or at least most of it) be said in a language that was also immutable and provide some continuity in the expanding Roman world.