The point was to just get the Avatar out of the way for another 16 or so years. Assuming they knew they were going to wrap up the war, the avatar being reborn wouldn't have mattered since ALL the world would've been under the Fire Nation's rule. Which, I imagine, would probably mean that the other bending disciplines would've been wiped out as martial arts. And with those gone, no Avatar could ever become fully trained and thus never be able to threaten what the Fire Nation would accomplish.
On the flipside, it probably would've just been more practical to just hold him until the war was over, then publicly execute him.