Maybe they did.
Back in the day, there was a DS9 episode where Martok mentioned the Klingons sending temporal assault fleets back in time to prevent the Empire's enemies from ever existing. Those fleets were of course never heard from again, and effectively their missions all failed (since everybody knows that history was not, in fact, changed).
So the Klingons probably just figured that trying to mess around with history was dishonorable, or a waste of effort. Or both.
Are you confusing DS9 with the Enterprise episode Carpenter Street?