Is it just because DF was developed on the fringe that it gets away with having infants and children that people use atom smashers on and have core game mechanics where monsters come snatch them?
Or is it something about the implementation that makes it drama-less to everyone?
As far as I'm aware anything that can happen to a Dwarf can happen to an infant or child.
Yup. You nailed it. It's all so weird and silly you can't take it seriously. Plus, the world is so chaotically hyperlethal - You might be mining for bauxite or whatever and the mineshaft collapses in to an underground cavern and then the next fifteen hours of gameplay are "The First Spider War: Dark years of horror and privation before things got really bad". And all you were trying to do with that game was make a screw-pump that moved beer between two levels of your fortress, but now your engineers are trying to divert the lava pipe in to spider hell before all your dorfs succumb to cave spider venom.
I haven't played in years, but from what I remember over the course of a few games, with things going horribly wrong in FUN ways, I stopped feeling like i'd failed when bad things happened to my dorfs and it was just like "Okay, the elephant thing was pretty fucked up, but the fortress survived and if we can just hold the zombies at bay until spring we'll get more colonists and then the elves will bring wood and..." and I just started rolling with it, trying to hold things together, reveling in my dorf's victories and building them very fancy tombs when they were torn apart by macaques or something. Actually, come to think of it, being able to bury the little weirdos probably did help. Like there was some closure or something idk.
The construction of fancy tombs is the essence of df. The game isn't fun if you're not taking frequent horrible losses.