I had an extended discussion with someone the other day where it took me a while to realize we were having different discussions. This tied back into how to make non-combat compelling, and we were talking around a specific example of persuading a duke to provide armies to support your cause.
The details surrounding such a thing are, while critically important in play, are not necessarily important to discussing it. This is exactly the sort of scenario I think can really sing since it boils down to one of the core dramatic structures suitable for intrigue - someone has something you want, and you need them to give it to you. The latter half of that is what distinguishes this from the similar action structure, someone has something you want and you need to take it from them. It may seem like a small difference on paper, but it's a gigantic one in play. Force is such a compelling resolution mechanism (especially in games) that its removal is a true game changer. For some people that change removes what they want out of play, but for others, it broadens the horizons of possibility.
This is not a value judgment. As much as I'm a huge proponent of expanding the game into arenas outside combat, it's important to remember that doing so does not implicitly create a better game, just a broader one. Bigger isn't always better, so if you have no interest in this stuff, then cool, just sorry to be wasting your time.
Anyway, to come back to the conversation, the disconnect we encountered was that she was talking about how to run the encounter, with the goal of persuading the duke at the end. I had, unconsciously, slipped into Amber mode, and had been talking about it in terms of getting the army. Those two things (Persuading the duke and getting the army) are related, but the difference is important to review. Getting the army is the ultimate goal of the exercise, and persuasion is one specific means of doing that. If you try to plan or one but do the other, you're going to get a weird mismatch.
Now, the reality is that a good GM needs to be able to handle both approaches. If your players are going to try to persuade the duke, that is perform a specific task, you need to be ready to run that well, especially I that seems the likeliest path. But if you only plan for that task, you'll encounter a problem when the players pursue a different solution (such as, say, assassinating the duke so his more friendly heir can take his seat). In most such situations, the players are focused on the goal (get the troops) rather than the task (persuade the duke).
It's not entirely accurate to compare this to strategy and tactics, but it's a useful comparison if only because it underscores that both are important to the prospective GM. If one is weak, the strength of the other might carry you for a while, but it can only go so far.
Anyway, there's a lot to drill into here, and it speaks directly to the issue of compelling non-combat, but I want to start by putting a flag in this, if only to remind GMs who finds themselves stuck to consider whether they're thinking about the tasks they're presenting players with, or the goals the characters need to achieve. Flipping which way you're thinking can be a great way to shake loose the brain.