Honesty, that's the same for nearly every open world rpg game out there.
Fallout 4: your son is missing, you want to save him and avenge your wife. But there you go, killing deathclaws and exploring the Wasteland like you're some kind of tourist.
Skyrim: you witnessed a dragon, which everyone believed to be extincts. Better tell about that to someone important as fast as possible, before dragons start setting everything ablaze!... Oh, wait, is that an ancient Dwemer ruin i see in the distance...? Well, i really need a pair of Dwemer boots to match my torso...
The Witcher 3: again, your daughter is missing, but Geralt is taking his sweet time between killing a monster and playing Gwent.
And so on.
While i do agree having basically a timed bomb inside your head is maybe the worst case of "exploring vs urgency", it's not like in other games this problem isn't a thing.
Maybe the only company who handles this fairly well is Rockstar: you normally are a criminal just trying to survive, get rich or rise in power; so every mission, even minor ones, actively contributes to your cause. But even there, once the main quests really start to develop (tipically between mid to late game), you always feel some sense of urgency.
Anyway, this doesn't bother me in the slightest. Never did, honestly. I WANT to have an important, life-or-death reason to finish the main quest, because main quests have to be epic and memorable, and like in every work of literature or in any movie, an epic quest requires an important reason to do it. But i even want to take my time doing it, because this is the very definition of an OPEN WORLD game: "a virtual world that the player can explore and approach objectives freely, as opposed to a world with more linear and structured gameplay" (from Wikipedia). APPROACH OBJECTIVES FREELY, including saving your own life. Does it make sense? Not in the slightest. Does it bother me? Nope.