I thought the argument was somewhat straightforward, but I can develop it a bit more:
Poetic meter in living languages is a serious aid to memory. Solzhenitsyn has a chapter about this in Gulag, Plato in Gorgias (?), and it’s obvious to anyone who has memorized much in the way of poetry or song lyrics.
The reason that such things stick in memory is, one assumes, that utterances with a euphonic and regular metrical pattern are easier for the brain to keep hold of than random strings of characters. (Some research has actually been done on this with numerical estimates of ease of recall, etc., but I simply think of the Huffman encodings; ymmv.)
Beyond poetry and meter, there is a fair amount of research on early language acquisition that seems to demonstrate that toddlers first pick up a limited set of sentence fragments that they then vary for all of their early language production. These fragments have been suggested to have specially euphonic characteristics.
Now, if you speak a language in a way that the poetry does not function, you are certainly also messing up the normal euphony of prose, and not only is it harder to memorize poetry, but also the base patterns of the language are not as sticky as they would be had you learned them from a native speaker, who would naturally intone these patterns in a regular, low-Huffman encoding, way.
Modern Greek, of course, doesn’t help because the basic patterns of the modern language are highly divergent from the ancient. In general reconstructions can be judged by how close they come to making the meter of poetry “catchy” to the ear and tongue.
There you go, an argument, and maybe even logic.