You are partially right in that Italian is not perfectly phonetic, but it's in such a different league from English that (100% - Italian) is a rounding error with respect to (sanity -English) ;-)
Still, Italian is still perfectly phonetic in writing: can you imagine never having to ask how to spell a town name, or a family name? Can you imagine a word where spelling bees do not exist because they could make no sense? If you hear it, you can spell it.
By the way, your example of "tʃ, dʒ" is spot on, as in you cannot guess how a Z character is to be read, but in practice very few people ever notice. Concerning "ŋ", I think only Italian linguists know about it as a separate phoneme.
You are wrong, instead, about "ɲ": "gn" is always pronounced as in "gnocchi".
As a native Italian, I'm convinced that using the Latin alphabet without embracing phonetic spelling can only be driven by idiocy ;-)