Stance dice in story mode present a few problems because the 'price' of stance (delay and exertion) does not always hold up. Sometimes delays and exertions are irrelevant if there is no pending action or time constraint. This can be worked around with a little creativity though. I wouldn't allow stance dice in story mode unless I was prepared to assign appropriate and relevant penalties from a delay or exertion.
Let's say the players have found a locked box, they take it back to town and that evening the thief tries to pick the lock. If she uses reckless stance and gets exertion, so what? She's gonna go to bed right after. Granted there are banes on reckless dice as well, but what about conservative? What does a delay mean, when she's got all weekend to unlock the thing before they need to catch a boat to Marienburg?
If you have house-rules regarding long-term fatigue and stress, then reckless stance may be okay. For the delay, you might rule that if she takes all weekend before pulling it off, so she can't get anything else done.
I allow this sometimes, but you've just got to keep an eye on the ramifications of the exertions and delays.