I really like the idea of a game that cycles once a day, so that you don't have to be glued to your computer 24-7 in order to keep up and enjoy the game.
But I see two problems.
First, with the sheer size of the map, players could reach a point in the game where they have thousands of units, and managing those units would take hours and hours. Not exactly sure on the numbers, but my point is eventually you could reach a point where you simply don't have enough free time to keep up. Not sure what the solution is, or if there even is one. (If I got to that point, I would probably try to find someone to share my account so that we could each do half the work.)
Second, with the game processing everything at 4 a.m. (Central), and with everything being processed in order from the previous 24 hours, players who can log in at 4:05 a.m. Central time have a huge advantage because their attacks will be processed first. (Personally I benefit from this, because I live on the West Coast and work until 1 a.m. Pacific, so I go home, eat something, watch TV for 20 minutes then log in, but that's beside the point.) Changing the time that things get processed just shifts the advantage from one group of players to another, but I'm wondering if it's possible to make the game process things starting at a random time. (The processing would still happen at 4 a.m., but the order in which things would be processed would be different each day. One day, for example, it might start with a move made at 7:24 am and loop back around, and the next day it might start at 10:17 p.m. and loop back around.)