Generally, classical Latin is even closer to letter-by-letter phonetics than Church Latin, which is influenced by Italian. For example, "caesar" is "k-eye-sar" in classical, "chehzar" in Church.
The phonetics that basically follow the intuition of an English speaker is legal Latin, where "bona feeday" becomes "bone a feyed". But I doubt lawyers have any use of "filioque".
"But I doubt lawyers have any use of "filioque".
Certainly not Greek Orthodox ones (even though I was a classics major)!
Since the last post, I have failed to come up with an example, and so am forced to admit, you are likely right.