What is your position, Qimmik, on the utility of writing conversational Latin (or Ancient Greek?)
I'm not sure what you mean by "conversational" Latin and Greek and what your aims are. I think the traditional composition textbooks-- Bradley's Arnold and Sidgwick--that train you to translate complex passages of English prose into Latin or Greek, and give you help with style and vocabulary, are very useful for mastering the languages at a level sufficient to read, say, Cicero, Tacitus, Thucydides, Demosthenes, Plato, or any poets in either language with some degree of fluency. These books generally show you how Latin and Greek modes of expression differ from English (19th century English, to be sure, but they're still useful), and they teach you idiomatic expressions.
I think that attempting to conduct written conversations about everyday matters in the ancient languages may be fun and there's nothing wrong with setting that activity as your goal in learning the ancient languages, but I question whether it's something that will give you much help if your aim is to engage with the more difficult ancient texts.
In trying to write ancient Latin or Greek as an exercise to improve your command of the written languages, it's important to look up nearly every word (apart from "function" words, pronouns, etc.) in a good Latin-English dictionary (Lewis and Short or the Oxford Latin Dictionary) or the
good Greek-English dictionary, as applicable--i.e., a dictionary that distinguishes among various usages and meanings of each word and provides an ample selection of illustrative quotations from ancient authors--to make sure your own usage is attested in an ancient author. (This is also true if you are trying to learn to write fluently and idiomatically in modern languages if you're not a native speaker, but it's harder with dead languages because there is a limited corpus of texts, particularly in Latin.)
I suspect that those who attempt to conduct written conversations in ancient languages don't always make the effort to make sure their usage is correct, i.e., conforms to ancient usage. Also there is a risk that they will pick up bad habits from others whose knowledge of the languages is not much better than their own.
Let me be frank about this--and from what I've read on this site, I suspect my views are in a minority. The fact is that Latin and ancient Greek are dead languages. There are just a few people alive today who, after many years of intensive study begun in early adolescence (at the latest) and extensive reading of ancient authors can write these languages in a manner approximating that of ancient authors. We can access these languages only through limited corpuses of texts, many of which are in very damaged condition. We live in utterly different social circumstances from the people who spoke and wrote these languages as living languages, and we think about things in radically different ways. Under these circumstances, "total immersion" in the ancient languages is simply not possible.
The ancient languages, like other "foreign" languages, aren't easy to acquire if you want to get beyond a very elementary level. Mastering a foreign language takes a lot of effort, not all of which is necessarily pleasant. And the ancient languages pose unique difficulties.