I'd never use it. I can't see how it would benefit me to have the battle start and end at some random time, not of my choosing. We plan our battles when it's most convenient for our players. When the battle time starts becoming inconvenient, we move it. I'd never turn the start time over to my opponent.
You probably imagine that you'd hit the BATTLE READY button and the battle would start, but far more likely, your opponent won't have hit their button and now you're stuck waiting for an indeterminate amount of time for it to begin sometime in the next 24 hours.
It's 5pm on Friday and you're matched for war. You brewed troops and got all your CC's filled and you're ready to go at 6pm. You hit your BATTLE READY button and nothing. Ok. They're not ready yet. You check back in a half hour. No battle. Ok. Give it another half hour. Still no battle. It's 7pm and you're headed out to dinner with friends. You keep checking your phone all through dinner, but still no battle. You check again before bed. No battle. You've missed out on raiding, because your army camps are full of battle troops, even your CC. So you use them on a raid. Maybe that dragon spam was a little overkill for a 105k elixir raid, but better than nothing. You set your barracks and request hogs for your CC to get ready to battle again tomorrow.
You go to bed, wake up, and check again. Someone attacked you and cleared out your CC. Stupid hogs. Looks like you'll have to request again. The exclamation mark! Battle has begun. Wait. It looks like your opponent pressed their BATTLE READY button at 4am your time. "Why are we battling at 4am? This stinks." They have a crushing lead, nothing you haven't beaten before, but your members aren't particularly enthused about risking their resources now that they know what they're up against. "We should just save our elixir and dark elixir for next war. These guys are too good." A couple remind you, "I told you I wouldn't be around much on Saturday. If only the battle began on Friday. Or even if it ended on Sunday, I'd be able to get both my attacks in. Why are we battling at 4am?"
You deal with all the arguing and complaining. You may have to boot someone when the war is over, but you manage to rally your troops to mount a counter-offensive. Things are looking good. It's really close and your clan still has attacks left. Some still have both left, but maybe they're waiting until the last minute. If they don't use their attacks, you'll have to boot them, too. If only you could stay up all night until 4am to see how it turns out. Maybe you'll set your alarm clock. You wonder how many other players will set theirs. You wonder why you're the only one who cares how this battle turns out. Hey did someone just attack without CC troops and no spells? "Sorry, Chief, it was either attack now or not at all. Didn't want to get kicked. Why are we battling at 4am?"






