Regarding duels, it seems to me that it's just a result of the fact that it's supposed to be 1-on-1, with no outside help whatsoever, magical or otherwise. But court isn't 1-on-1, so applying the same restriction isn't intuitive.
I think it's more than that. A duel is supposed to decide who is right . Now, there are problems with that concept -- from a game perspective, it's obvious that "I'm right and you're wrong" has zero mechanical effect, while "I'm a Kakita and you're not" has a lot -- but that's the idea. Once you ask the kami to help out, though, you are blatantly acknowledging that the deciding factor will not be who's right and who's wrong; it will be who has more advantages in his favor. There is no way you can allow magic in a duel and maintain the fiction of what a duel is supposed to represent.
Court is the exact same. I think there is a misconception of a lot of people as to what "court" is in Rokugan. It is mostly a place of challanges,
Uh, what?
As in my previous comment, I have to ask: what's your basis for this statement? L5R fictions? Because I've done quite a lot of reading about historical societies, Japan included, and boiling everything down to "it's one on one fights" is not anywhere close to a good description of what court is really like. The notion that doing stuff there is comparable to the sacred, ritualized space of a duel, the tool by which Tengoku supposedly makes it clear who is in the right, is absolutely croggling to me -- as Fumi said, it's more like a skirmish, if we're going to make a comparison to a fight. And nobody has ever suggested that it's dishonorable or inglorious to use spells in that kind of combat. Even if we take your framing of court: why is it okay to supernaturally interfere with your bushi friend's physical fight against another bushi, but not okay to supernaturally interefere with your courtier friend's verbal fight against another courtier?