RTS's don't use dedicated servers for hosting games. That includes Warcraft 3.
The only games that have company dedicated servers for hosting games are MMOs.
Most first person shooters (counter strike and such) let people set up their own servers for people to connect but that wouldn't work well in Demigod.
In Demigod, we can't get away with prediction because it would be incredibly frustrating online for people. For example, when the rook picks a target and hammer slams, that entire action might take 3 seconds. 3 seconds is an eternity if the game isn't peer-to-peer.
In a game such as Counterstrike, what you see on your computer isn't the same as what is happening on the server. That's why you can end up with cases where you are "sure" you shot someone but they didn't die because it only looked liked you shot them but according to the server, you missed and so no HP is deducted.
Even a game with true dedicated servers such as World of Warcraft,, they have to set these servers up by region in order to mitigate the latency issue I just described above. But doing that in Demigod isn't practical because, for example, right now there are 1073 games of Demigod being run. That would be a lot of servers (even virtual servers) to be set up around the world.
There's nothing inherently wrong with peer-to-peer except that it makes getting the initial connection more difficult. But the connection issues on day 0/1 had little to do with peer-to-peer but rather the actual dedicated servers that handle the match making being overwhelmed by connections from sources we had not anticipated.