It wouldn't surprise me if the element ones are Rinnegan mutations too. Just as the Rinnegan is better than the sharingan but the sharingan's best versions have some advantages, perhaps the element kekkei genkai are more specific variants of it's ability to let people use elements.
Of course, we don't necessarily know that all of them come from the Sage's line at all. It may just be the kind of thing that happens with the genetics in the world. Rinnegan did pop up on it's own after all. They also seem the simplest conceptually- the genes that make someone naturally aspected to one element or another exist for multiple elements (or are otherwise linked) in the same person.
Originally posted by Demonic Phoenix
Ya know, this has got me thinking. Hashirama was the only person to have the Wood Element naturally. It's obvious Hashirama had kids, as he has a grand-daughter. Yet Tsunade does not have the Wood Element. So either those advanced natures cannot be passed down, or Mito Uzumaki's genes interfered?
I think both Haku and his mother had Ice, so it seems they can pass down, but don't necessarily do so.
Hm, we don't really know of any clans revolving around a combined element kekkei genkai, unlike the eye ones which seem to always pass down. (Amateur generic hour to follow) So it may they are normally recessive and only show up occasionally.
It could be that there's a general set of genes for element aptitude, some dominant and some recessive, and kekkei genkai happen when two (or in Mei Terumi's case, three) of them all manage to activate in one person. So (using upper-case for dominant and lower case for recessive, and Wi / wi = Wind, E / e = Earth, Wa / wa = Water etc.) someone might need WaE to have mokuton, while Wae would just be a water user who could also use Earth (like perhaps the Second Hokage, his brother).
Or even more complex than that. We know it's not just one pair, since it's possible to have three.
But whatever the case, it seems likely that while the eyes can be passed over in their entirety, elements are *probably* a combination of the parent's genetic traits in respect to elements, so there's more chance involved and a lot of people likely have an incomplete set needed for the kekkei genkai.