Compared to Classical Latin for instance, I can sort of intuitively see how a "purity" comparison might make some sense. The grammar is more rich and precise, suffixes and prefixes attached to primitive roots are more regular in terms of meaning. Meaning is very decoupled from word order, which allows much richer possibilities for rhyme and prose. If the restored pronunciation is anything to go by, then the pronunciation is very regular. Then again I'm not a linguist.
I would say it's like arguing whether Python is more "pure" than Perl. They're both Turing complete, they express very similar concepts but I'd wager most people would concede that Python feels "purer".
Isn't the 'purity' of Latin due more to the fact that we just don't have much data on the languages that informed it? I'm sure Latin borrowed heaps of words and grammar from other languages, but those languages are mostly lost to history now, since the people who spoke them didn't conquer and hold the Mediterranean for one thousand years.
I would say it's like arguing whether Python is more "pure" than Perl. They're both Turing complete, they express very similar concepts but I'd wager most people would concede that Python feels "purer".