A peace deal has to be set to come into effect at some point in the future so that the message can be spread along a very long line of soldiers, some of whom may not have regular radio contact or be in small pockets. Not only do you need time to inform everyone, you also have to set it at a specific time after everyone is informed, so that you can make preperations with that in mind - for example, getting ready to recover stranded wounded after the ceasefire.

That would be incorrect for 99% of cases in the war. Commanders were trying to get into the best possible position for continued bargaining and/or the armistice was broken.

Who wants to be the position that's overrun because at the last second, the other guy decides to storm your position?

There was no way to instantly let everyone know at 5 AM that they should stop fighting; some hours were surely needed to get the word out.

If anything the "cute quote", or poetry of the "eleventh hour, ..." phrase helped to shorten the killing. Lloyd George had instructed that the armistice should be set to come into effect at 2:30 PM (so that he could announce it triumphantly in Parliament), but Admiral Weymss, British naval representative in the negotiations, took it upon himself to bring the time forward to 11 AM to minimise the loss of life, as well as for the poetry of the moment. (The Prime Minister was not pleased!)

The surrender was only signed at 5am that day (Paris time). It is reasonable that it would take some time to inform all troops and prepare for a ceasefire.

There were many injustices and crimes during the course of the war but I would not go as far as to say the Generals let fighting continue for their amusement.