Points of interest in real life can be within a day's journey, forests can be tiny (though they typically have different names), and "towns" (as in populated settlements) can have about 5 buildings or less...
Days is possibly an exaggeration, but it certainly wasn't as easy to walk to places as it is today, especially if you're wearing heavy armour and need rest breaks.
What would be the odds of finding a blacksmith in a 5 building town? Or a tavern? Or any other merchant? We're not talking about the same thing here.
And to top it all off people have been known to survive a lot of punishment and it isn't unusual for someone to die AFTER a battle (Some famos examples of people who were riddled completely with arrows and bullets). So "probably" nothing, you will probably have to stab them a few times before they stay down.
Sure. But dying from your wounds after the battle is still dying. The only thing that's remarkable in those cases is that it took so long, and the fact that it's remarkable is the point. Most people in similar circumstances would die more efficiently. Deep stab wounds would almost always be fatal (eventually).
