Oh wow! This is some amazing food-for-thought. I'm currently studying the Thoth and haven't read anything about VAU until your post. I can see a lot of this concept at play in the Thoth's Swords suit now that you mention it. Time for more research
The pattern goes: IHVH, repated four times for the four suits.
IOD - Fire - Wands - Knights
and
HE - Water - Cups - Queens
come together for
VAU - Air - Swords - Princes
which transmutes into
second HE - Earth - Pentacles - Princesses
I believe the Princesses are referred to as both ending the suit process and beginning the new cycle, which is why they're particularly potent cards. I also believe they're the only court types not attached to astrological decans, but are instead the "pure" essence of their elements. The Princess of Disks, the last card in the fourth and last suit of the process, is often seen as the last card in the deck and very powerful.
This is of course based on binary genders and sexual reproduction. You have some decks such as Daughters of the Moon, a feminist deck, that completely replacs the usual 4 courts with 3 of Maiden, Mother, Crone, and removes the Emperor and Hierophant cards, which it considers traditionally overtly masculine, absorbing their meanings into the Empress and Priestess cards, "returning the masculine powers" (book's words) to the respective goddesses, since male emerges from female in their perspective.
Sol Invictus the God Tarot turns the courts into a linear process of Awakening, Quester, Nurturer, Master. It's similar to the Thoth but embodied as stages of a man's life and growth.