It will be that much harder for one country to get that far ahead.
I'm still confused a bit:
First nothing about your plan prevents numerical imbalance. So it's already quite common for one side the get twice as many players as either of the others. Someone just recently posted a screenshot of a common example.
Wouldn't what you are suggesting destroy ebb and flow because:
1. You can't form alliances any more. Every team has to attack the other in predictable locks step. Right? wouldn't that lead to less interesting dynamics?
2. It is possible each of the smaller teams must take a base of the larger team next, but the larger team have enough numbers to block them. So couldn't you have a deadlock condition? Each of the smaller teams can't take their next needed base from the larger team, yet they aren't allowed take any other?
3. Wouldn't what you suggest create bizarre tactics like once team A takes a base from team B, team B is now free to temporarily remove all forces from the A-B front because they are not allowed to attack again until after they've take a base from team C?
It kind seems to me you are going the long way around the barn to create a pseudo 2-sided arena. You're starting with 3-sides and forcing each side to alternatively pretend it's only two sides and ignore the third side. You'd just be throwing in a bunch of extra complexity and create additional perverse states.
In my opinion, 2-sides with aggressive ENY and side limitation if necessary, would make a lot more sense.