I tend to be sceptical about unrelenting grimness—because I try to make my game world logical.
"The world has been enveloped by a fog of doom for a hundred years". Okay, all people are dead from starvation. The last cannibals died decades ago. Next world!
The world has to be—has to be—sufficiently benign that children will, on the whole, survive into adulthood. Think about the hazards you put into your world. A 10% chance of killing each inhabitant each year? The population is now plummeting.
I think the way to evoke the setting you want is to have good areas and bad areas, benign conditions and crises. It's the contrast between the two that'll evoke the feeling you want. Happy kids, educated populations, active trade and thriving farms will just serve to highlight how grim things get when the systems of society break down.
A war, plague, fire or flood, a bad ruler, a subversive cult, or a band of wandering murder hobos become unutterably grotesque when your characters see its effects on ordinary people.