A few reasons:
Latin syntax does not depend as heavily on word order as English and the Romance languages do. Furthermore, it doesn't use prepositions nearly as much, and there's no articles ("a" and "the"). All of this means that there is way more freedom to position words for a variety of effects.
For instance, the famous first words of Vergil's Aeneid are arma virumque cano, which means 'I sing of arms and the man.' cano is the word meaning 'I sing,' and its position at the end of the clause is perfectly normal for Latin. But this means that Vergil can declare his subject as the first word of the poem.
(If you look at English translations of this line, you'll see how translators try to match the effect, usually be creating somewhat awkward English.)
As for the fetish, part of that reflects an era when anyone who had a significant amount of schooling meant studying a great deal of Latin. These poets provided the touchstone for taste and style, which had a self-reinforcing effect.
But in my opinion, Latin is infinitely better for poetry than English. English is much clearer than Latin for prose, though.
If you're really curious, someone wrote a book to answer your question:
https://www.amazon.com/How-Read-Latin-Poem-Cant/dp/0198788126