For a start I think it would be fairly hard to win a war with only 2 countries, because as the bases got less on one side ALL pilots would be there around the action, this would also lead to lag, warps and framerate hits, as it would be very very busy in the sky.
Also this type of gameplay would follow a very set formula ie: one side would get the upper hand and steamroller the opposition this would lead to very linear gameplay that operated on one level.
But with three it means you have to defend other front, which in turn spaces out pilots over a wider area and as a by product it offers up two types of gameplay at any one time, offence AND defence,
Also we would miss those times when you have one side down to 3 bases (say rook) and your trying to win and all the time the knights are catching up, and if they gain a base more than bish the gameplay changes so that you have to protect the last rook base and get a knight one back.
In my opinion 3 countries leads to a much better game dynamic with a gameing style to suit everyone.