This sort of thing is what broadly divides role-playing into two styles or approaches: treating it more as a game that the players are trying to win, and treating it more as collaborative storytelling in which the players and the GM are trying to create a compelling narrative. Nothing but sorrow comes from a mismatch between players and GM in this regard. There's nothing better or worse about either; they're just very different experiences.
Joss Whedon once said that spacecraft in "Firefly" travel at the speed of plot. That to me captures perfectly the narrative approach to role-playing. The GM decides how long the trip should take, within broad parameters of plausibility and consistency, and the players take that as a given and create their narrative within that framework. "Gaming" players would instead start pulling out rulebooks and calculators to second-guess the stated duration.
In a narrative campaign, the merchant character would leave her sidearm in her quarters because that's consistent with how such a person would behave in real life, and thus adds narrative depth and realism to the unfolding story.
In the old Avalon Hill WWII tactical-combat game "Squad Leader", I vividly recall a scenario where an American platoon was hit by a surprise German attack while the soldiers were in line for dinner. They were unarmed, and had to get to where their weapons were before beginning to fight back. That small piece of realism made that scenario one of the most emotionally compelling wargames I have ever played. The experience went from optimizing how counters moved around a map to some sense, however slight, of the panic and desperation of real combat.