Et Latine Conundrum

 The Romans had been speaking Latin for a thousand years before the Church came to power in the Empire. Many of the "other" Romance languages developed simultaneously with the big ones.

Latin didn't change because it was highly inflected, all languages change over time. Not every word can be changed according to all of those variables, some of them apply to nouns and others to verbs. That is NOT why Latin is used to classify species, we just needed a common language for it.

Some modifications are even more complex than Latin with two extra cases and 3 extra tenses (times). 

So, complexity is not really why the language died. We can express ourselves much more efficiently. English achieves its range of expressions with new words and phrases, we can achieve most of this with just grammar, plus we can add new words and phrases. The language is too complex to spark wider interest, but complexity can't be the reason because the roman empire was much stronger and widely spread as opposed to Croatian, or even Czech and French which uses very complex grammar.

You can learn the words of another language, but that doesn't mean you know the order in which they go. Some words don't exist in other languages, and so you must be poetic when you speak. For instance, a famous roman senator ended his speeches with "Carthage must fall." In our present language, there are many ways to say this. 

I would have said: "Carthage must be destroyed." You could also say "Carthage must die." It's possible in ancient Latin that the word "die" had another meaning, and the word "destroy" never existed at all. 

After the fall of Rome, Latin ceased to be about preserving some sort of replica of the classical language and became more of a conlang that was meant to serve as a functional lingua franca for all of Christendom.

I think if you want Latin to remain a functional language like it was in the Medieval, Renaissance and Early Modern periods, you'll have to accept, not necessarily grammar or syntax changes, but certainly new vocabulary and perhaps new phrases. 

In my opinion, it is necessary to keep Latin standardized. It should be allowed to add new constructions to the language to better fit modern usage, so long as it doesn't detract from the value of Classical Latin or inhibit the ability for Latin speakers to read all Latin literature.