I think Fallout: New Vegas did it excellently. You had the main premise "I wanna find the guy who shot me for carrying a special chip" is a more "relaxed" premise rather than the very urgent "I NEED TO FIND MY INFANT SON!"
Finding the guy who shot you, for possessing some kind of special chip, is more a detective story that is about clues coming up through time and exploration, nothing urgent like if they added "I wanna find the guy who shot me AND plan to nuke New Vegas, knowledge of this is why I was shot!!"
They really need to learn to write a story like that if they wanna keep this "Oh look a sandbox do whatever you want" gameplay. And then of course learn to write side quests to do that makes people give a piss.
I don't agree. A chase is always an urgent quest, because otherwise you risk the trail will go cold. The lower stakes of the New Vegas chase may reduce the importance of the quest and the emotional investment, but it doesn't actually reduce the urgency.
Also, Fallout 4's main quest basically loses its urgency (though not its importance) when it becomes clear that years have passed and the son is no longer an infant. Once you take down the merc guy, then someone trying to roleplay has plenty of excuse to go explore.