Though you question role-playing in Fallout 4, you might really want to figure it out for yourself by playing the game, and in that case don't read further!!
---- --- ---
Okay so in previous Fallout series there were some tasks in a post-apocalyptic world. And the killing was good! Anything wrong with that? Yes, and that's the idea to Fallout 4, that's why you need a son!!
You were living fat in a civilized neighborhood with McDonalds tatooed on your stomach happy with your family and son. Role-playing is not about choosing your family, because that's given from start. And you don't object to people just because they happily have a kid??
And in Fallout 4 you accidentally enter late post-apocalyptic period after 200 years' rest. And as a family-man you still need to provide security for the kid, though most others seems to have given up on that. So therefore you immediately begin to build settlement with others as you need safety for the kid, which might be just around the corner!
And while meeting others on the road you also immediately initiate them to settle, because the more settlements - the more secure your settlement is between them!
But then it happens that law-less raiders attack the settlement, and as a family-man you need to immediately put an end to that to secure home for the kid! So you dig out the camp of those raiders and find out, that some are just instinctly attacking because of hunger, and they accept to join the settlement. But other raiders with terrible backgrounds who have long enjoyed senseless killing (like "you" in previous Fallout versions) they can obviously not fit into the settlement, which neither has any prison. So they'll just have to be eliminated!
And that's the point with this Fallout story that a civilized world can afford criminals with prisons and McDonalds while a post-apocalyptic world can not!! Why your impression of lawlessness in post-apo.. is probably ... correct!