I will do what you have not, which is to understand the document you posted.
SV:
Siquidem non sine divino consilio illud evenit, ut qui sermo amplissimam gentium consortionem sub Romani Imperii auctoritate saecula plurima sociavisset, is et proprius Apostolicae Sedis evaderet (3) et, posteritati servatus, christianos Europae populos alios cum aliis arto unitatis vinculo coniungeret.
My translation:
And accordingly not without counsel [roughly assent or providence] it happened, that the speech [language] which had united the very great partnership of peoples under the authority of the Roman Imperium through very many centuries, this [language] both came out as the special language of the Apostolic Seat and, having been guarded for posterity, joined the Christian peoples of Europe with each other [alios cum aliis] in a firm bond of unity.
This directly precedes your quotation. That is, the historical nature of Latin makes it suitable to Catholicism, not the structure of the language itself.
As an
aside, the encyclical mentions “Neque hoc neglegatur oportet, in sermone Latino nobilem inesse conformationem et proprietatem; siquidem loquendi genus pressum, locuples, numerosum, maiestatis plenum et dignitatis (4) habet, quod unice et perspicuitati conducit et gravitati.”
This unique (“unice”) structure, of course, developed historically as well, and there is no reason that it cannot be paralleled or exceeded by another language.
The real quotation that disproves your claim is the following:
Etenim Ecclesia, ut quae et nationes omnes complexu suo contineat, et usque ad consummationem saeculorum sit permansura…, sermonem suapte natura requirit universalem, immutabilem, non vulgarem.
These reasons – universality, immutability, non-vernacular-ness – for preserving Latin within the Church have nothing to do with Latin as a language.
Immutability is important:
Si enim catholicae Ecclesiae veritates traderentur vel nonnullis vel multis ex mutabilibus linguis recentioribus, quarum nulla ceteris auctoritate praestaret, sane ex eo consequeretur, ut hinc earum vis neque satis significanter neque satis dilucide, qua varietate eae sunt, omnibus pateret; ut illinc nulla communis stabilisque norma haberetur, ad quam ceterarum sensus esset expendendus.
Translation:
Furthermore, the Church’s language must be not only universal but also immutable. Modern languages are liable to change, and no single one of them is superior to the others in authority. Thus if the truths of the Catholic Church were entrusted to an unspecified number of them, the meaning of these truths, varied as they are, would not be manifested to everyone with sufficient clarity and precision. There would, moreover, be no language which could serve as a common and constant norm by which to gauge the exact meaning of other renderings.
In other words, Latin is a good language because it is dead. This is a historical development. Latin, if it were still in use, would be unsuitable because it would be mutable, as the encyclical states explicitly after that quotation.
You are wrong, quod erat demonstrandum demonstratum est.