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Chess on a 2D board can be too complex for the human mind to understand.
Pushing the game to 3, 4 or more dimensions, while often a fascinating
mathematical study, can be frustrating for the variant gamer, who just
wants to *play* a really neat new game. But the lure of higher D chess is
irresistible. Recent instances of this have been seen in new CVwiki entries
on 4D chess, a new 3D 'Name Game' by Charles Gilman, and comments on
Alice Raumschach and Chesseract. It's a fascinating topic that produces
games that are very difficult to play. But that doesn't keep us from
coming back to the topic again and again. I've done a half-dozen higher D
games myself. Being kind, I'll say most of these games don't get a lot of
play. But play is exactly what most of us want to do with a new game. So
what's the problem? 

The problem is the number of possible moves pieces have, on higher D
boards. And it really comes down to a question of diagonals [which relates
to the power of a piece]. Ben Reiniger has some numbers in the CVwiki that
illustrate this rather well:
N 	wazir 	knight 	ferz (1,1,1) (1,2,3)
2 	4 	8 	4 	- 	-
3 	6 	24 	12 	8 	48
4 	8 	48 	24 	32 	192
5 	10 	80 	40 	80 	480
6 	12 	120 	60 	160 	960

What happens is that the game becomes chaotic; players have no way to
forecast the state of the board even a few turns in advance because there
are so many possible moves.