I think that idea is friggin brilliant. It definitely ease the pain of losing a fortress, especially for, as you said, new players. That'd be especially important as the steam and itch releases will open up the world of DF to newcomers, a lot of them learning about the game from steam, not knowing what to expect as a newcomer.
The problem, as stated before, comes when you start adding in multiple achievements for losing to different things. Now, you don't just get an achievement for losing a fort, you have a checklist. Oh, you want achievements? Well, you haven't lost to a goblin invasion yet. So go make a disposable fort lose to goblins on purpose. Now make one lose to necromancers on purpose. Oh, and how does the game know when you "lost to a necromancer", anyway? What if your fort is slain by zombies, but the last dwarf is actually killed by another dwarf tantrumming? Well, you already had a tantrum loss, so no achievement for you, start over and do it again.
Having one achievement for a fort crumbling is fine, but you guys are forgetting the reason
why "Losing is Fun" is the tagline. It's supposed to be encouraging you to say that losing isn't the be-all-end-all of the game. (Especially because the OP's "lose" conditions are all fortress mode, so apparently you shouldn't even play adventurer mode?) There should be an achievement for reclaiming a fort to try again, or for sending an adventurer to the site of one of your old fallen fortresses. There should be an achievement for your adventurer reclaiming an artifact one of your old forts made. There should be an achievement for your adventurer finding a masterwork whatever in the markets of another town besides your fort, just to see how far that dresser you sold to the human caravan actually traveled. There should be an achievement for building a new fortress on a cave that had been cleared out by your adventurer.
Achievements shouldn't be "lose because that's all Dwarf Fortress is, just losing because you dumbasses apparently can't learn the game", they should be hints and encouragements for exploring aspects of the game that someone who only plays by generating a world to make one fort then do nothing else try doing other things like retiring the fort, playing an adventurer, and unretiring later.