What are the pros and cons of the Erasmian pronunciation?

For this answer, bear in mind that there are three current pronunciations of Ancient Greek:

• Erasmus’ reconstruction of Ancient Greek phonology, as modified in practice for teaching Greek in Western schools: Pronunciation of Ancient Greek in teaching
• The scholarly reconstruction of Ancient Greek phonology: Ancient Greek phonology
• Modern Greek pronunciation applied to Ancient Greek (“Reuchlinian” pronunciation): Johann Reuchlin

I will differentiate in the following between Erasmian (as taught) and Reconstruction. Erasmian as taught tends to make the following concessions. (Happy to be corrected.)

• Usually stress rather than pitch accent
• Often fricatives rather than aspirated stops
• Nativisation of diphthongs
• Some distortions in the German version
• Even more distortions in the French version

Pros of Erasmian:

• It’s a stable system with respect to the various periods of Greek. Greek pronunciation varied by era: Homeric was different to Classical Attic, the dialects  likely differed, and there was significant change between Classical and Koine Greek. With Erasmian (or Modern Greek), you only need to learn one pronunciation. So long as you don’t care about historical accuracy.
• It’s somewhat close to the scholarly reconstruction of Greek; so a lot of the phonology and morphology of Ancient Greek makes much more sense. With Modern pronunciation, augments and contraction are just magical mappings between letters, that you learn by rote. In fact, they make as little sense as English spelling, for pretty much the same reason.

Cons of Erasmian:

• It’s not quite fully there with the scholarly reconstruction of Greek; so some of the phonology and morphology of Ancient Greek still doesn’t make sense. Particularly with diphthongs, and aspiration, if your local Erasmian doesn’t do them accurately.
• Extreme variability from country to country, because of the concessions each country’s teaching system makes to the local language.
• Speak in Erasmian to a Greek, and they’ll look at you like a space alien. Or even worse, a German. Now, if you’re speaking Ancient Greek to a Greek, you deserve to be looked at like a space alien. But they will genuinely have no idea what you are saying, or what language you are saying it in. Even diehard turncoats like me cannot help themselves from reading Ancient Greek out with modern pronunciation, if they speak Modern Greek: we need all the help we can get.
• It’s quite far from Koine. Koine was still in flux, and some critical changes were underway when the bit of Koine most people care about (New Testament) was spoken. But overall, Koine was much closer to Modern Greek than Homeric.

In conclusion, the  reconstructed Greek I’ve liked the best. Most recordings of Ancient Greek in scholarly reconstruction are of Greek poetry. Because they stylise (some might say, overdo) the pitch accent and the quantity, they end up sounding like yodelling Martians. My favourite reconstructor does this too when he reads  poetry; but mercifully, he also reads prose. And when he reads prose, he is the only person I’ve heard who sounds like he’s speaking a human language.

It helps that he’s Greek. His phonology is not Modern Greek, mind you; but I think it helps a lot that, at least in this recording, his intonation is. I give you Ioannis Stratakis:

Herodotus, Histories 1.1-4 (reconstructed ancient Greek)