I say pronounce Ancient Greek as you wish, just be aware of the other modes of pronunciation. I use the reconstructed one, but I can certainly see some advantages in using modern Greek, which I hope to learn it once I’ve mastered the former.
Imagine learning about compensatory lengthening, Grassmann’s Law, etc. while using a MGk pronunciation. How to make sense of nominal declensions (logos, acc. pl. logous), principal parts (menw, emeina; leipw eleifqh), … These regularities would play out very differently in a different system. Just to be clear, I do not advocate ignoring current Greek as a language, with a literature, etc., and naturally, its own phonology, but like Italian it deserves its own separate study. And that’s what it gets. That Ancient Greek as a language gets more attention from many is an accident of history. And a final personal note: Being forced by my teachers of Modern Greek to get every last accent right in class as well as casual conversation really helped me become equally attentive to accents in Ancient Greek.
Alright, although it seems like you’re saying these alternations make sense only when they’re phonetically motivated in a transparent manner, but that’s certainly not true in all cases – for example the long vowel corresponding to ᾰ is often η and not ᾱ, and even with compensatory lengthening, it’s not obvious in the usual pronunciation that ο should lengthen to ου and not ω. Basically, I don’t see why understanding how these patterns came about depends on the pronunciation you use (except in the extremely rare case of those who think the pronunciation has never changed in any way).
Then again, that they make sense in that way doesn’t seem all that crucial. When you learn a language you learn what the alternations are and where they occur – anything else is learning about (the history of) the language and not learning the language itself. I mean, it’s something that most native speakers wouldn’t know about, it’s not something that’s taught in the teaching of modern languages – do you need to make sense of Modern Greek λόγος, acc. pl. λόγους? I don’t deny that it can make memorizing declensions and so on easier (and still, you can take advantage of knowing these patterns no matter how you pronounce the language) but it just seems to me it wouldn’t be a factor in making a pronunciation a bad idea. Although, for me, pronunciations of dead languages cannot be bad ideas in and of themselves but are bad ideas only with respect to the setting in which you’re using the language.
A large amount of these books are available at Google Books and if you get a google account, with some judicious searching you can end up reading quite a big chunk of them. You might want to check them out that way to see if you’d find them useful.
Thanks for your attention. I have just found a bookshop where are available and not expensive enough. Anyway, I will check what you have pointed.
On behalf of all the Greeks that know how Greek was pronounced etc but choose to pronounce it the modern Greek way, my heartfelt thanks. I am sure my professors at the University of Athens (who also pronounce ancient Greek the modern Greek way) would like to thank you too.
With due respect to Helma, and the knowledge she brings to this forum, I think that Modus raises a good point here.
To give a small Dutch example; Do the young Dutch students get taught where the 's at the beginning and the s at the end of 'smorgens and 'savonds come from?
The case of Italian and Latin is different compared to Modern Greek and Ancient Greek. In Italian the orthography is quite different, in MG remained the same. Many (if not the majority) words remained the same, though the pronunciation has changed. One has only to learn that the plural of words ending in -os is -oi (pronounced -i) with some exceptions in cases where the gender is neutral or feminine. I don’t see what’s the difficult and what advantages you get if you pronounce it -oi. If the orthography in Italian remained the same as Latin, I don’t think one would be able to read Italian, but will end in a mixture of Italian and Latin, closer to Latin than Italian with a modern pronunciation. E.g. dottore will be written doctore pronounce doktore.
I understand the case of poetry is quite different, though for me poetry goes more through the meaning of the words and the meter or the sounds are of no importance, but then I am not trained or fond of ancient poetry and less of the pre-classical one.
I find it more important if two Hellenists come together and use same pronunciation and understand each other. No one reads Shakespeare the way he did. He wrote also poetry. Do we lose anything by rendering his plays in a modern way? I don’t think so. We continue to admire the meanings of his words and the composition of his poems strikes more important. Now think what a mess would be if everyone speaks Shakespeare the way he likes or is able to do, just because there is no point of reference and just describing an a-sound as close or open is not enough.
Recently I worked together with a Japanese student. Honestly, I couldn’t understand a single word of his English. He learn English is Japan, from books and Japanese teachers who probably also learn their English from books. At the end of the day we ended to communicate with notes, or remain silent. In the written form, his English was perfect. A language one learns only by hearing and imitating the sounds, never by description of a sound, no matter how close and accurate that description is.
I’d like to add my two drachmas.
Pronunciation is not arbitrary. Especially in poetry, poets write their words because they produce certain sounds, often rhythmically organized. By not reading aloud a Greek poem as it was intended to be heard, the poetry itself is lost, making the whole endeavor rather pointless.
I think it’s extremely hard for native speakers of the modern language to give a historical pronunciation, whether it be for English readers of Shakespeare and such or Greek readers of Plato. For non-natives, it’s just another foreign language, so I would recommend a different course of action for people who do not speak modern Greek yet.
The point of vowel quantity, raised by another poster, is apparently also not a problem.. Well, if no problem matters, then you should just do what you want to do, but not make an argument that it’s the right thing to do. I won’t quibble with personal preference:-)
Should you want to read up on what we know:
Horrocks, History of the Gk language and its speakers, tries to give phonetic approximations for the passages from all eras that he discusses in his book. Devine and Stephens ‘Prosody of Gk Speech’ give the most uptodate treatment. Not for the faint of heart!
hi, for me the main thing to focus on is the quantity, not the quality, of eta: the latter varied over greece but the former didn’t, as far as i know (if it did, please let me know, that would be interesting)
also worth noting that quantity applies also in prose: dionysius of hal actually scans some attic prose from thucydides and demosthenes, worth checking out.
i just mention this because i’ve only ever heard one “real” classicist in real life, and he didn’t distinguish quantity which i found a bit strange, cheers, chad 
Well I didn’t personally said anything about what way one should use to pronounce ancient Greek. Different reasons prompt different people to adopt different pronunciations. A really bad idea though?
I do find it strange to say that not pronouncing say AI as the ancient Greeks did in one region or another in one era or another doesn’t mean that you can’t make sense of morphology really. I would like to argue that there are professors and other academics who know a lot about ancient Greek and how it was pronounced through the ages and still use the MG pronunciation.
As for “extremely hard” well, I don’t know. I mean yes, you do have to overcome your instictive pronunciation of delta as /δ/ for instance but extremely hard? I never found it to be so to tell you the truth (nor any of the other Greeks who know ancient Greek and we’ve talked about this issue. True, the “hue”, the “overtones” are modern Greek but then I have yet to hear anyone pronouncing ancient Greek with any kind of pronunciation that was devoid of his/her native languages “quirks” .