Picture a fortress that has slain a plethora of megabeasts, raids of every race, has legendary squads of warriors that can thanos snap a forgotten beast out of existence and are ready to take on the circus. You get close to that candy, however, you want to build infrastructure to make it possible for your warriors to fight one clown at a time, so you build a winding series of hallways. Somewhere along the line, one of your haulers you didn't even bother to notice was getting a bit stressed because the cook has been building instead of cooking lavish meals, the alcohol's been running dry and he hasn't prayed in a while. Suddenly, he throws a tantrum and beats another dwarf to near death. Now that dwarf is stressed because he almost died, so he throws a tantrum and beats several dwarves up, who themselves become stressed. Then, the original dwarf goes berserk and one of your military dwarves has to kill him, and now that military dwarf is stressed because he just killed another dwarf. Soon, more dwarves are becoming depressed, looney, and going berserk. One of your legendary military dwarves with masterwork steel armor and weapons goes berserk in the middle of your meeting hall and slaughters half your fort before the other military dwarves can take him down: However, they are stressed about killing other dwarves too and seeing all that death, so some of them go berserk. When the dust clears, you have a few military dwarves - if you're lucky - who are all depressed and experiencing traumatic flashbacks every 5 seconds and peasants with miles of corpses to clean. Your fort of 200 was rapidly reduced to 12 lucky dwarves who have 188 corpses to clear out. That, Toady, is the problem with stress. It stacks too much and too quickly.
Not to mention, there's also the memories of a sentient being that died in front of someone years ago haunting them forever and causing them to stop whatever they're doing for a while. I once had a dwarf who was attacked by a cat when he was gelding it and that became a 'traumatic memory' for him, so every 5 minutes or so (50 fps, 30 gfps) he'd just stop doing everything was doing and 'experience horror' for a while.
tl;dr it lasts too long and can pile up quickly. Ntm all this puts a deadline on your fort and usually the average DF player can run a fort for 15-20 years before it collapses due to a stress spiral. I've had forts where I was reckless and killed bards and tantrummers in front of people last shorter, up to 5.