What's the point of attack board inversion? In tri-dimensional chess some rule sets allow for the attack board to be moved from the peg on top of the main board to the peg on the underside (as long as the attack board is unoccupied). What is the point of this inversion? Especially since some rule sets deem it okay to ignore inversion rules.

Inversion seems redundant since the attack board's level under a board is the same as the level if it's on top of the board below. i.e. KL under neutral board is equal as KL over white's board.
The Star Trek set I'm familiar with has connection points for the attack boards at the corners of the main boards, but not elsewhere.   So you can have the attack board above the middle board in 4 spots (the corners), or inverted from the upper board, halfway across the middle board.

If the middle board is labeled a1-d4, then the attack board can be placed 'upright' at the outside corners of a1, a4, d1, and d4.   It can also be placed inverted at the outside edge of a3 (near a2) and d3 (near d2) beneath the upper board.

You can also invert a board without moving it along the file.  Moving it between boards requires at least a 1 'peg' move along the file.