The second I saw DT mentioned I knew we'd have a little battle here
Personally I'm very much in a 'live and let live' on it (and similar programs). I used DT (and it's spiritual predecessor dwarf manager) when I started, then at one point there was a question of who would update it (and nobody seeming to step up) after a major release and there was talk of it being abandoned. I decided then that I'd just play and figure it out, I haven't gone back, not because I don't like DT but because it's easy enough to manage a fortress without it because (as mentioned) once you get enough dwarves usually it starts to just work itself out and I'm not terribly anal about my fortress (I'm ok with lots of statues of dwarves surrounded by cheese) as I'm mainly in it to survive wave after wave of enemy assault.
That said, I'm totally cool with people playing it for different reasons or with different tools, it's not my problem.
If somebody said "The game is unplayable without DT" I may beg to differ because, clearly, it is not. However this thread is about what would make it unplayable "for you" in which case saying "The elimination of DT" is totally fair game.
For me.. Well eliminating the pause feature would certainly do it but that is awfully unlikely, I mean making you have to play in braille or having the game text be in a complex cipher would too but I don't see any of those happening.
For a realistic change, I would say a complete breakdown of the military system; I mean ok, I get that it's not ideal now and some people even consider it 'unusable' but (not to start a new kind of argument) I use it extensively and it works for me (and I typically use it as my only line of defense, no walls or traps against Fortress Defense and other monsters without danger rooms or other similar things). But if it were to progress to a state where (to me) it became unusable it would kill the game because setting up challenges to try to overcome (which often involve combat) is the main reason I play.