For instance, the English sounds of "J", "W","Th", and "Ch" are for the most part unused in Hebrew. (Although as an exception, I've seen a Yemenite Chazan use some of these sounds while reading the Torah).
Does the particular phonetic makeup of the language mean that only the included sounds are capable of being holy? Is there some other significance to it?
First of all, Yemenites, Iraqis, and some other Mizrahim (hello) preserve the Minhag that developed in Late Biblical Hebrew and was widespread until the Late Masoretic Era, to pronounce all the soft בגדכפת letters distinctly, which includes pronouncing ת without a dagesh as “th”.
In Biblical Hebrew, before the exile, there were no soft letters. So no bh/v, gh, dh, kh, ph/f, or th. All six letters only had their “hard” pronunciations.
Additionally, ו was always W, never V. ז, ד, and ת were on the teeth instead of the roof of the mouth. ח and ע each had two pronunciations—one like Mizrahim pronounce them, and the other slightly fronted. ט, צ, and ק were also pronounced the Mizrahi way. ר was either an Italian trill or a Spanish flap/tap. Sin was different from ס; air was directed around the sides of the tongue. In the Gileadite dialect of early Biblical Hebrew, Shin was pronounced TH in some words, and SH in others; but in most dialects, Shin was always SH (as it is now).
If only these sounds are “holy”, and other sounds can’t be, we’re in trouble. Almost nobody pronounces the letters in their original form. Additionally, many words in Hebrew have clearly undergone some evolution from an older form with some different or extra consonants. I’m going to assume (i.e. I know) that Hashem planned for these inevitable changes, and still accepts our תפִלּות and לִימוד תורה.
This probably means that non-Hebrew sounds have the potential, at least, to be holy.
Another possibility—I don’t know the source at the moment, but I recall reading that angels fix mistakes in pronunciation as they take our words to שמים. If non-Hebrew sounds are not holy, this may be the way Hashem accepts our Hebrew service.
Either way, Hashem knows what He’s doing.
As for the significance—As I write this, I’m not yet a Kabbalist, and I doubt most people on this site are either. But I do know that each letter corresponds to a certain fundamental abstract concept. So the original sound of each letter is likely connected in some way to its fundamental meaning. Using ו as an example, something about the /w/ sound has to do with connecting things (like a וַו, the Hebrew word for hook).
On a similar note, maybe sounds that didn’t exist in Biblical Hebrew correspond to non-existent concepts that were never created. Or maybe they wouldn’t correspond to any concepts, and the fact that those sounds exist at all is simply a result of the shape of the human mouth. Or maybe they do correspond to concepts that were actually created, but those concepts weren’t necessary for the creation of anything else. Those are three theories for you off the top of my head.
Quoting R' Avraham DeBalmash: "lashon hakodesh contains all possible movements of the mouth, but there is controversy as to what letter signifies which sound", on which he elaborates between differrent methods.
The yemenites have (some of them at least) kept the original pronounciation intact, where today many if not most Jews have lost some of the more obscure and uncommon sounds in their native country to an extent.
According the to answer here Hebrew alphabet sounds were selected by Avraham avinu who knew 70 languages of the world. In fact, part of his mission to spread the belief in one G-d was to show that after the episode with the Tower of Bavel people of different nations could still communicate by building dictionaries using letters expressing sounds. Therefore, in the times of Avraham, Hebrew letters could express all sounds, and since then the languages diverged to include other sounds.
