I'm running a tabletop RPG and out of rules convenience I just made it so any injury that isn't fatal or very serious, such as losing a limb, will naturally heal within a day or so. Now this hasn't really come up so far but I feel like this *should* come up and I have a feeling that this would have some, if not significant, impact on a setting. 

The question more specifically can be stated as such: In the course of a narrative that isn't strictly about society and culture or the daily humdrum of life but merely one that takes place *next* to it, what resulting factors from the above scenario are significant enough to bleed into the narrative? 

As for some relevant details, the rest of the setting is low to mid fantasy, medieval technology and magic. The regeneration is entirely powered by magic and you can ignore things such as the *how* and *why* of it, it simply works.