[I apologize to others I had to send my answered to Pavlos via e-mail.]
You wrote: The accent you suggest as "ancient Greek" is in fact the so-called "Erasmian accent," i.e. a scholarly attempt to reproduce ancient speech devised by Erasmus a.k.a. Desiderius (1469-1536), a Dutch scholar.
First, the new Greek accent is one of my suggestions, too. It is more familiar to me, personally, too. I cannot ignore other accents, however.
Next, the so-called "Erasmian accent" is in fact very close to the ancient Greek. The reconstruction is reliable enough.
You wrote: This invented accent has a very strong latin pitch to it, as some of the Greek letters (eg. theta, delta, gamma) are very hard to pronounced by most western Europeans.
I cannot understand you very well. The so-called "Erasmian accent" is not just invented. Rather, it is a reliable reconstruction. Latin has been used in that reconstruction. It would be so successful without Latin evidences. The other source for that reconstruction is the traditional Greek spelling.
I think that the new pronunciation of theta, delta, gamma is too hard for most Europeans. The new gamma is approachable by Greeks only. People speaking French, Italian, German, Slavic are not capable to the new delta and theta. In contrast, the Erasmian accent is familiar to all.
You wrote: What the true accent of classical Athens (let alone Sparta, Crete, Macedonia, etc) was cannot even be a matter of speculation! Think of an English language scholar in 1500 years trying to reconstruct what English sounds like, when there are today diverging accents such as Oxbridge, Cockney, South African, Noo Yawk and New Joysey, Southern, Jive/Ebonic, and DownUnderish!
I cannot agree here. Each language exists as a set of dialects. Even now, the new Greek is a set of dialects. So is English now (consider British, Australian, several Americans accents). So was English at Chaucer's time. So was Greek at Classic times.
Nevertheless, we can say which accent is now English and which is not. We can say which accent is Greek and which is not. Similarly, we definitely can say which accent was Greek at ancient times and which was not. For instance, at ancient times (B.C.), an accent without respect to the length of vowels definitely was not Greek.
You wrote: There is however one universally accepted fact: Greek words that begin with a consonant and have a "rough breathing" (daseia) originally has a slight "h" or "s" hissing to them, mostly lost in modern Greek. This is why the Greek word for water, YDOR, became HYDOR in Latin (as in hyrdoelectric), YPER became HYPER or SUPER, EXIS became SEXUS and so forth.
Actially, there are many universally accepted facts. You consider a consonant 'h' which existed in the ancient Greek and Latin (and also in modern English and German) but was lost totally in modern Greek (and also in modern Italian, Spanish, French). In very ancient times, when a commonly acceped form of the Greek alphabet was not established yet, there were different versions. Some people used the letter eta to denote the consonant 'h' and Romans borrowed that letter with this value, others preferred to use that letter for the long vowel 'e' and used to skip the consonant 'h' in writings. The latter version prevailed in Greek. Later, when Romans wished to learn Greek, the currently known diacretical marks were invented (daseia, accents) to help Romans in mastering Greek tongue. Actually, the daseia was a little 'h' in the beginning. So, the daseia can be considered also as an additional letter to denote the consonant 'h'. That consonant was heard in ancient times.
You wrote: This is why the Greek word for water, YDOR, became HYDOR in Latin
That word was HYDOR in Greek (see above). Greek alphabet does not contain a letter for the consonant 'h' and so Greeks wrote simply YDOR and later a daseia before YDOR. Roman alphabet does contain such a letter, so Romans wrote that Greek word entirely, HYDOR.
You wrote: ..YPER became HYPER ..
See my explanation for HYDOR above.
You wrote: ..YPER became HYPER or SUPER..
Most probably, SUPER was the oldest form in the (IE) proto-language attested in Latin. In the transition from the proto-language to Greek, initial 's' went to 'h' very often (consider also HEPTA/SEPTEM/SEVEN, HELIOS/SOL/SUN, etc.) Hence, the sentence "Greek YPER became Latin SUPER" is not true. I would say, the word "SUPER" from the proto-language became "HYPER" in Greek and did not change in Latin.
You wrote: My personal bias is that it is more correct to read classical texts using use the contemporary Greek pronounciation rather than an accent devised by a well-meaning Dutch scholar.
I think this is a matter of taste, not of correctness. Using the ancient pronunciation is also correct. I would not promote any option.
You wrote: After all, Greek is a living language for several millennia, that has evolved in a pretty linear fashion. It never had to be resurrected from scratch, as in the case of Hebrew.
So is Latin. It has evolved to French, e.g. Should we use the modern French accent for texts in classical Latin?
You wrote: Why? Pretty much for the same reason that we would rather Chaucer today using a contemporary English accent rather than some devised Pythonesque manner.
The case is not the same. The English language as attested at Chaucer's time was not of any importance and had not any influence anywhere else than in England. So, the English accent at Chaucer's time is not of any importance today - we can merely use the modern accent.
In contrast, ancient Greek was of great importance and had a great influence all over the world, at least all over the world known at that time (I exclude America, China, India, most of Africa.) Greek was the language of Christianity - the New Testament was written entirely in Greek. Hence, many Greek names and words related to the religin went into Latin. In western Europe, however, Christianity was promoted in Latin. Hence, many Greek names and words were frozen in their ancient pronunciation.
Let us assume I was asked for the pronunciation of the name Barbara, a Greek name. I would be correct in my answer to give both the ancient and the new Greek pronunciation: Barbara and Varvara. Which is correct? At ancient times, it was definitely Barbara. Saint Barbara (3rd century) called herself Barbara, most probably.
You may probably argue that in ancient times there might be some Greek dialects where the accent was Barbara and others where it was Varvara. Surely, the transition B to V did not happen suddenly. Now, it has been Varvara in all modern Greek dialects since 5th century approx. Definitely, it was Barbara in all Greek dialects B.C. Most probably, in the first centuries A.D., Barbara was changed to Varvara in some dialects and later, by the 5th century A.D., that accent prevailed. I can suppose that the transition B to V (and also PH to F, and also other similar changes) was caused by the great number of people with native Aramaic being turned to Greek tongue in their converting to Christians.