There is a little something in what you say, I think, in that a universal language (“dead” or otherwise) does act as a kind of symbol of unity, and the idea of Catholics around the world united in not merely the same ideas in prayer but the same words, rhythms of language, is a wondrous thing. However I don’t think it makes the prayer any more effective.
(It’s also world pointing out that the Church didn’t ‘choose’ a ‘dead’ language for anything - Latin was the vernacular everyday language of the Western Roman Empire, as Greek was in the East. For a long while early in the West, the Mass was celebrated in Greek (I understand). Latin is only “dead” now because the vernacular has shifted to languages evolved from Latin (French, Italian, etc), or others like English or German. By the time the Rosary was formalised Latin was the language of law and church, because a longer time ago, it was the language everyone knew, and the Church just never caught up until 1969…it’s why “the Mass has to be in Latin” argument is kind of ridiculous because even though on an aesthetic level there is much to be said for it, the reason Latin started to be used in the first place was so everyone could understand it, so there is therefore every reason to now use local languages, although of course there is the felicitous symbolic value of using the same language everywhere, as you point out!)
This trend of thought is worth expanding.
The Israelites wrote the first 5 books of Scripture in Hebrew. Considered by them a Sacred language.
However after their 2nd diaspora in Babylon, the returning 2 tribes mostly spoke Greek. As this, was the lingua franca of that they. About 300 years before Jesus was born, there was clamour from the people, because when they went to the Synagogue and heard the readings, they did not understand a word of what was said in there.
A commission of Rabbi was established to translate the books of the people (The Scriptures) to Greek. The resulting book was the LXX or Septuagint. Some people on this board dispute this, but the majority of Scripture experts do believe and agree on this.
Now Christianity started in an area where Greek was the language for commerce.
However when St. Peter moved to Rome. Here the situation complicates, because the people in these lands did not speak Greek. They spoke Latin.
Hence the word “Vulgo”, it means “Common”.
Funnily the Google translator gives “translation” to the word “Vulgata” but that is totally incorrect.
How can you go from the root “Common” to “Translation” is beyond me, but I digress.
Therefore the Church, took the same approach that the priests of the OT 300 years BEFORE Christ took and ordered the Scriptures to be translated from Greek to Latin.
As the Church expanded to the ends of the Earth, as commanded by Jesus, She continues her duty to give Her treasure to all, by overseeing that the Bible be faithfully translated in the languages used by Her faithful and “other” denominations.
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And God bless you