In the guidelines for storyline quests, Jenna says that quest flavor isn't the actions the character takes "to do the quest", they're fun actions or scenes "you can imagine a character performing while on the quest". Similarly, many of the anytime quest variants end up being "your character acts a certain way to show they're on the quest", even if they're not how the quest advances in-universe. This is really cool, because it makes the quest feel like it's happening in the narrative, without needing to spend scenes on it directly beyond what would be interesting and fun.
For example, an example quest in the core book is Cleaning up an Old House. In a pastoral game, you might want to spend a scene or two showing the actual process of cleaning up, but even then it probably gets repetitive unless it's a particularly weird and wonderful old house. The storyline version is focused on scenes around the house, but there are also two other versions that are focused on, basically, mentioning or establishing that you're working on the house in unrelated scenes. One is for coming up with theories about how something you encounter in an unrelated scene could help you with the house, and another is for explaining things (like being tired or having tools) in terms of your working on the house. Both of these seem like solid ways of establishing that the renovations are taking lots of your character's time and attention if the game doesn't want to focus on this activity on-screen, and that approach is generalizable to all sorts of activities.
I've been noticing a lot of similar things watching Buffy, and I think it's a pretty common technique in TV shows and such. You don't have to watch Buffy take the SATs; you briefly have her worrying about them ahead of time, and you show her getting her scores later. Willow mentions in different ways in different episodes that she's studying to be a witch before her witch studies become the major plot point in an episode, which makes it seem much more believable than if it was just sprung on us suddenly (while waiting until it gets interesting to show it on-screen). It feels like this sort of dynamic is both an effective type of storytelling when you have an episodic narrative with time skips and in-universe down-time between epicness, which applies to both Buffy and many Chuubo's campaigns.
In a way, it's similar to what I was saying before about worldbuilding, in that what a character's doing off-screen doesn't feel real until it's established in play. You sorta assume that no-one's doing anything interesting off-screen unless you've got evidence otherwise. Some D&D rules optionally suggest that you might not get leveling-up benefits until you've had downtime to learn it (not that I expect this usually gets used), but I don't feel like it feels real, even with downtime, if it's completely abstract. Requiring it to be brought up in play, giving other characters the chance to roleplay responses and ask questions, seems like it makes the process of learning a new skill or spell or any other sort of off-screen character development feel more a part of the story.