You're asking this question because JWs have been taught to look at Scripture through the lens of the Watchtower.
For those of us who are Jewish, we do not see the "regularity" you mention. For instance, there are enormous spaces in Torah where God never gets addressed with or connected to the Tetragrammaton. Add to this the fact that Jews have always seen the words EL, SHADDAI, ADONAI and other similar terms as equal names of God. The JW claim that these words are but "titles" is simply false. Like the Eskimo people who have a number of different names for "snow," these so-called "titles" and even substitute words like "Heaven" are SHEM or Names of God.
The odd preoccupation the Witnesses have with the Tetragrammaton cannot be more far removed for Jewish language and culture. It is a Gentile invention as the use of the name of deities was a common heathen and pagan practice. The heathen petitioner believed the attention of their deities could be granted by utterance of their divine names, and that the same could withhold answering prayers if their names were not used or pronounced correctly.
The Tetragrammaton is, on the other hand, a self-designation that defies being labled. The Name is a circular definition: "I am what I am" or more specifically "I am defined by what I am and the fact that I define all." Whereas the Hebrew word for "name" (SHEM) means "handle," referring to a means of grasping and controlling the one named, the circular reasoning or meaning behind The Self-Designation is meant to defy being labled or handled or controlled, as if to suggest that nothing we can utter can rightly be something to call God.
While the name may appear some 6000 times in the Hebrew text, it does not do so consistently. The Psalms, the official liturgical prayers and hymnal of Judaism, often dispenses with the Divine Name completely. Numerous Psalms never use it, beginning with Psalm 40. The famous Psalm 45 used by Christians as prophetic of Christ is totally lacking it.
The book of Esther doesn't even mention the word "God" throughout, not to mention the Tetragrammaton, whereas recently discovered extant Hebrew manuscripts of Sirach or Ben Sira (so called apocryphal by the JWs) contain it. And while the second generation of LXX manuscripts demonstrate that Jewish scribes were experimenting with ways of incorporating YHWH into the Greek text, the oldest Septuagint texts have spaces with dots and the latest used KYRIOS as the finalized manner chosen by Jews to represent the Name.
The consistency is imaginary among the JWs who seem far too bothered to do any real and sufficient critical study into Jewish uses of names, both divine and mundane. So on the one hand, if the New Testament was supposed to be some "addition" to the Jewish sacred texts, the striking absence of the Name, now written some time after the LXX finalized substitution as the best invention for Greek transmission does not seem surprising being that the New Testament is a product that grew out of the Second Temple era where such a practice was considered respectful and honoring.
But the fact remains that the New Testament was never seen or intended as an additional volume to the Tanakh. I'm fact, except for the Torah, Judaism differed widely in what it cherished as Scripture. Remember, for Jews the Bible is the PRODUCT of a true religion, not its basis. The Scriptures did not validate or support the Jewish religion and its claim to God. On the contrary, it's claim to being started by God at Sinai outweigh the texts Judaism produced and the importance these acquired.
And the same goes for the Christian New Testament. Had it not been for the issues raised by the heretic bishop Marcion, there may have never been a set of Christian scriptures. It was Marcion who invented and introduced a Canon of Scripture and introduced the idea of proof-texting into Christianity from Gnosticism. Christianity knew no Scriptures but the Jewish writings, and even then there was no settled canon. Judaism had yet to see the Tanakh as a single volume at the time, and the Christian books would not be canonized until the 4th century. Judaism and Christianity had not remained static, so how could a collection of their texts spanning generations be expected to?
Expecting the New Testament writers to have revived the practice of employing the Hebrew Tetragrammaton for the Divine Name (long after the translators of the LXX had decided on using substitutes) among scattered writings never originally intended to be one collection is the invention of the etymologically ignorant.