Ah, okay, I gave a quick once-over to the articles. I understand now. It has nothing to do with the actual number of children.
But as far as I can tell, all of these different methods are just various ways of doing the same attempt to deal with the impedence mismatch of the data-format-to-storage-format.
The article from MySQL seems to advocate per-event high-processor cost (recompute the tree every time you touch it) to save on storage and retrieval costs. ie - It may be faster to do a SELECT BETWEEN than a LIKE.
So, what I gather then is that there are many ways to attempt to solve this problem, all of which have their advantages and disadvantages, none of them inherently better than the other?