This is not always a good thing.
Sure, scrambling away from the bad guy gives your character an immediate purpose, and a motivation that doesn't even have to be spelled out, but a whole rush of such scrambles do not form a story, just a maniac sequence of episodes. ("Of simple plots and actions the episodic are the worst. I call a plot episodic when there is neither probability nor necessity in the sequence of episodes.")
Smuggling in an overarching purpose is somewhat easy, as long as there are a few lulls, and points at which character choices are driven by the purpose and not the threat of the moment.
It's his motive for this purpose, why he wants that end point, and what it will secure him, that gets interesting, because even if his motive is survival, as it is when running headlong from the ravening wolves, it isn't obvious merely from his running from wolves. He'd do that even if his motive was to clear his father's name, locate his long-lost brother, show up his evil uncle. . . .
If the character has a chance to leave the danger, that's a good point, but it's not always practical to have such a moment; it would affect too much else of the plot. Some other point to slither in the moments of reflection on what it's all about are needed -- and real fun to slither in.