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If 8x8x8 is too big, and 4x4x4 is the smallest 'real' chessboard in 3D,
then Raumschach 'goes small', controlling diagonals by having close edges
which limit movement and thus attack potential. It also uses only 10 pieces
and 10 pawns per side, far more handle-able than 5 or 10 dozen. Still,
there's a degradation of the pawn wall. Bishops can capture opposing pawns
on the first move, showing gaping holes in that wall. To close that up,
you'd need 2 more rows of pawns 'above' the white pieces and also
'below' the black pieces, giving 4 rows of pawns - twice as many as
pieces - per player. That's kind of ugly, in my opinion. 

Let's take a slightly geometric look at pawns and pieces, and their
structures. In the beginning of the standard 2D game, a line drawn from
anywhere in your camp [back rank] to anywhere in the enemy camp
[opponent's back rank] must pass through 2 pawns, minimum, at the
beginning of the game, one friendly and one enemy pawn. For higher D games,
when such a line is drawn, how many does it pass through - 3, 2, 1  or no
pawns? The line: is a chain of cells that touch each other, whether at
corner, edge, face [etc]; goes through the minimum number of pawns
possible; and is drawn as straight as possible [no extra wiggles]. With a
symmetric setup, the answer, for 3D, is either 2 or 0, and the 0 line would
have at most 2 bends in it, in reasonable, and reasonably simple, setups.
What 0 means is that pieces have a way around the pawns, making them less
relevant.