Okay but the Den Mother doesn’t actually want any of the mechanical outcomes associated with winning a duel of Influence. Nor can she actually rationalize any of them. No Resources to gain, no Faction to invest in, no Disfavor (no factions at all, this early in the game), no stains to remove other than what might crop up in the fight.
There’s also the matter of the duel types being necessarily different. So I get that dueling for influence is what you do when influence is what you want in the fiction, and I get that the resources/favor/disfavor choices are there to add mechanical oomph to your fictional intent. But say you’re fighting For Blood and your intent is murder. Obviously you’re not going to get what you want until you’ve beaten them mechanically and achieved the kill result (Final Blows, no allowances). So that’s kind of different. I’m not even sure what intent “for Honor” even looks like beyond the mechanical benefits.
So…”for Blood,” you get to maybe narrate first blood into the duel’s outcome but you don’t get to kill them until you’ve earned that mechanical result. “For Influence” I guess you do earn whatever in-fiction outcome you wanted plus additional resources and favor if those are even part of the fiction (otherwise just lots of strain defense). And dueling “for Honor” I can’t figure out what one might intend in the fiction, but the mechanical benefits seem tightly wedded to, well, clearing your honor.