The problem is that whatever rhythms it had are lost except for the broadest outlines and a smattering of specifics, and none of that can be taken entirely at face value. The Latin we study now has the rhythm we bring to it.
Or, here’s another way to think about it: I am reminded of Jurassic Park. They only have fragments of dinosaur DNA to work with, so they splice them into the DNA of currently living creatures. Well, the DNA that is spliced into gets to express itself, with wacky consequences, but it’s still the only hope mankind has to ever get eaten by a dinosaur. But I mean we’re not talking about a total crapshoot here. It’s not a coincidence that certain living creatures bear a resemblance to dinosaurs, and even with the inevitable differences it would still recover more information about what a dinosaur was really like than any amount of looking at the DNA fragments in a dish.
I have no knowledge of languages that aren’t Indo-European, and that may make a difference in what I choose to look into and what I conclude, but much of prosody arises out of certain physical constraints of the articulatory apparatus. A lot of similarities between English and Latin prosody can be tied to these constraints – the time it takes to enunciate different vowel sounds (as mentioned earlier), the syncopation of unstressed syllables, the shifting of vowel quality in special circumstances. If I investigate this further, I’m sure I could make a very strong case for this, but feel free to explain where I’m going astray here.
Basically, though, just the similar manifestations of prosody in response to biological apparatus common to humans suggests that a language like English would not be a bad stock to graft what fragments we have of Latin prosody onto. The result would be anglicized, but alive.
And it’s not just English. I haven’t gotten directly involved in this Living Latin movement, but I’ve chatted on the Locutorum at the Schola website with Italians and Germans, all of us expressing ourselves in Latin. All of them are presumably also learning the same reconstructed prosody that I’m learning, mutatis mutandis, with their own native prosodies filling in the unrecoverable gaps. And these voices, especially since it’s possible to hear them over the internet, will ultimately mesh – exchange memes and such.
So, I guess you are probably right. That is, I don’t believe that there are rhytms left from Latin that can be recovered without grafting them onto our own, but I do agree that the rhythms that emerge from doing so will tell us more than a handful of written records could about what Latin must have sounded like. Yet, I’d still like to start out with the best information we can glean.