And again, all we see in YE is the Federation side. For all we know the Klingons were on the verge of collapse but were willing to die fighting to the death whereas the Feds weren't, and the final battle at Earth (if the Feds didn't surrender) wouldn't left the Klingons with nothing either to hold the Empire together.
It's like the Federation-Zeon war in the Gundam series. They fought and it seemed like the Feds were on the verge of surrendering, but then a Federation General escapes and lets the Fed High Command know that Zeon exhausted all its resources in the biggest battles and were putting up a false front to trick the Feds into surrender. Which led to a longer war where the Feds win.