What you call "classical pronunciation" is really at best an approximation of the ancient Greek pronunciation, but mixed heavily with English (after some frolicking around in Latin). As far as I know, this is limited to English speakers only.

For example, π is pronounced "πι", or probably closed to "pee" in modern and in ancient Greek. It's never pronounced like "pie". Same with all letters that end with "i", for example "φ,χ,ψ" (pronounced as phee, chee, psee, never rhyming with pie). T (τ) was never pronounced as "ta-oo", either, not in ancient nor modern Greek.

There are differences between modern and ancient Greek of course. For example "β" (beta), originally pronounced more like it's now in English, only with a longer "e", while in modern Greek it's more like "vita")

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Modern Greek is, frankly, irrelevant.

Ancient Greek is needed to get a full Western education, for reading some of our foundational literature properly.