In Trails in the Sky no enemy drops money after defeating them. Instead they drop Sepith, which is an important in-universe mineral. Every shop can exchange Sepith for money, but it also has other uses.
You'll probably ask "This kinda makes sense for monsters, but how does this make sense for humans?"
Well, the answer is that 'magic' in Trails in the Sky is based on technology (and its called Arts). To use Arts, a character needs to have an Orbment. In this Orbment you put in various Quartz'. Based on which and where you put them, you can use different Arts. Quartz are made from Sepith.
So I always think that the Sepith you get from humans is from some Quartz you broke when defeating them.
Also, the second game in the Trails in the Sky has some new and more powerful Arts and has you start with 0 Quartz' again. This is justified by giving your characters new Orbments because technology has advanced, and those Orbments require new versions of Quartz to work.
Trails in the Sky also has your questlog being an actual notebook that is being filled in by the main character, since that is required from the job.
Said notebook also features various handbooks and information, like which Arts require which Quartz.
Trails in the Sky also has explanations for how regular civilians can travel the lands when their are monsters crawling around everywhere.
1) they hire Bracers (think adventurer/police) for protection
2) placed along the mainroads are special lanterns that repel monsters (in fact, one early quest is repairing one of those lanterns).
3) most people travel via airship lines anyway