Origin used to (as in "pre-beta") do a lot more in this game - and there were more of them. It determined how many powers you could get and just how far you could enhance them (IE, you could have a few really strong powers, or many, but somewhat weaker, ones.)
I suspect it's one of those things that's baked down into the character so deeply that letting people change it would break far more than we suspect.
(As far as "what fits," don't assume you're going from a human standpoint - I have several non-human "natural" characters.)
Yeah I think in principle the Devs probably wouldn't mind allowing us some method to respec our Origins if it were somehow relatively easy to change. But like Memphis_Bill said there are probably too many non-trivial links to ancient parts of the game that applied when Origins played a more critical role.
Even now there are still the DO/SO enhancements and some low level mission arc dependencies that'd have to be accounted for. I just don't think it'd be as simple as changing a few graphic icons and text strings. My guess is that the Devs have generally decided it'd be far more effort than it'd be worth at this point.
Loth 50 Fire/Rad Controller [1392 Badges] [300 non-AE Souvenirs]
Ryver 50 Ele� Blaster [1392 Badges]
Silandra 50 Peacebringer [1138 Badges] [No Redside Badges]
--{=====> Virtue ♀
I realize it's a very minor aspect of the game, but I think there should be some option to change the origin of a character after its creation. I, myself, didn't understand the origins idea at first. For the record my main is not entirely human, so I assumed that would put him into the mutation origin even though that's not how he gets his power.
As far as how DOs/SOs would change with this, I can't imagine it's a very big issue with coding. Either convert them to the new origin's enhancement, or sell them like with respecing.