I really think that RJ wanted to have three female protagonists with different attributes and characteristics to be romantically involved with Rand. There was no need for LTT to have the same type of relationship because by the time the main story opens, he is long dead and reborn.

Yes, it does seem rather shallow, but I believe he wanted Rand to be with a brunette, a strawberry blond and a red-headed woman. I think their personalities went through multiple changes in his rough draft, so just like a child playing with a doll, he might have played with individual quirks and characteristics before deciding.

And as Tom says, there are sexual fantasies at play here. The same sexual fantasies that create The Feminine (or Masculine) Mystique and reduces (or uplift) a human being to the role of a larger-than-life archetype and an idol at the same time. I'm not sure that RJ can conceive of a woman as an entity unto herself without a romantic attachment - all of the female protagonists have relationships that are very much cornerstones of the story, and we meet very few single woman that are happy with their situation. This is an overall character trait, actually - there are very few single people in general that are personable, happy and well-balance with no interest in romance.

It just seems to me to be exacerbated in Rands' situation - very few of his relationships with his wives are well-developed and the indication I get is that he gets what he needs from the particular woman that is best able to provide it. Stranger still, in the story, though it's treated as comedy, he often makes comments in his POV that indicate he doesn't really know them that well, which is actually sort of sad to me.