I think it's a good idea, too.
Way too many times we get attacked at just the right time so almost none of us are on-line, other than seeing the battle replay & the message in the chat we wouldn't even know anything happened. Knowing when the battle took place would let us plan for defense against the next "sneak" attack in the wee hours of the morning.
Oh, & bobo I offer up a third possible reason for them not showing the battle time, which is simply that no one thought of it until now.