Well, not always dull, but often enough that I think it’s a problem.
By "running battles/etc" I mean a number of the various sequences where the player engages in core-quality challenges to raise a progress quality, and then uses that progress quality in a challenge to complete the story. Dueling the Black Ribbon, Hunting Dangerous Prey, Preparing for a Big Score, and so forth.
When I say they are dull, what I mean is that many of those sequences are almost entirely monotonous. Multiple options for increasing the progress quality are presented, but most of the time they’re functionally identical beyond slight differences in difficulty. If I’m choosing between a 57% chance to increase Casing and a 60% chance to increase Casing, I don’t feel like I’m making a choice - I just feel like I’m paying an action tax.
Not all progress-quality sequences are like this. I realized how dull some of them are when I recently started Engaging in Courtly Romance. I was surprised and delighted to see that the different options to increase Fascinating were providing results which varied beyond just slightly different amounts of Fascinating change points. Performing artistically gives me booze! Writing letters gives me stolen correspondence! I’d fallen into a rut of mindlessly pouring actions into heist or duel preparation without actually making any meaningful decisions, so it was nice to feel like I was actually being affected by my choice of preparation methods.
Offending sequences which come to mind:
Dueling the Black Ribbon. "Sparring with ring fighters", "Find out more about the Black Ribbon duelists", "Scout a battlefield", and "Exercise for rough health" all have difficulties between 74 and 82, only increase Running Battle on a success, and only increase Wounds on a failure. Why is this four different options? Why is their availability based on Airs of London? "Arrange a duel outside the Black Ribbon" and "Study the fighting styles of other duelists" increase Running Battle and provide minuscule side benefits (20 rostygold or 5 cryptic clues) on a success, and on failure they both increase wounds and decrease Running Battle; the progress they provide isn’t any better than the other options, so you’re risking having to spend more actions to make up lost Running Battle in exchange for a chance at pitiful rewards.
Hunting Dangerous Prey. Among the six options, the only possible rewards outside of The Hunt Is On progress are slight changes to forceful and subtle. On a failure, they all increase wounds and two of them also decrease THIO. Once again, their availability is Airs-dependent, despite having even less variety than duel preparations.
Preparing for a Big Score. Six options, four of them only increase Casing on a success and increase Suspicion on a failure. One can give 30 whispered hints and another gives a bundle of oddities, but those two options also decrease Casing on a failure so once more you’re paying for those rewards by spending more actions. They all cost three actions, so at least it’s less of a time-sink than grinding Running Battle or THIO. Also the Bundle of Oddities option ("The Decoy") spits you back out in the main menu without presenting a "try again" option, which is annoying.
There may be others, but those are the ones I’ve run into so far.
As for what could be done to improve those sequences, I have a few ideas.
Faster progress for varied preparations. Succeeding on a preparation method could give more change points if the last successful preparation was of a different sort, or if that particular preparation method hadn’t yet been used since the last time the relevant progress quality was reset (e.g. scouting a battlefield for the first time after winning a duel).
Different secondary benefits for different preparations. There doesn’t always need to be a material reward alongside an increase to the progress quality, but adding a chance to get something different out of each option would make the options meaningfully different. Small handfuls of common currencies (e.g. rats, glim, jade, candle stubs, silk scraps), rare successes for semi-common items (e.g. map fragments, intriguing snippets, first-city coins, fourth-city relics) or second chances, that sort of thing. Engaging in Courtly Romance does this nicely.
Get rid of progress losses on failures. If a success gives 3 progress, then every failure is an effective loss of 3 progress. Menace increases make sense, but tacking on an extra progress penalty is unnecessarily punishing. Failures resulting in not only the loss of the action spent on them but also the loss of another action’s worth of progress is anti-fun - a success moves you one step forward, a failure puts you two steps back.