Country X still has more players than Country Y.
Country X still has more players than Country Z.
Country X is not outnumberd by either enemy.
By that logic, Germany should have won WW1 in two weeks because its army was bigger and much more powerful than any of the
individual opponents it was fighting.
By that logic, if you put the starting 5 for the Celtics on the court against the starting 5s for both the 76ers and the Nets, the Celtics should win since they are the best team and since they aren't outnumbered by either the 6ers or the Nets.
Of course, that logic is nonsense. 5 = 5, sure, but 5+ 5 = 10 and 10 > 5, it'll be a slaughter. The Celtics would get stomped, even if you mimic AH by saying the 76ers all have to stay on one half of the court and the Nets all have to stay on the other half.
Likewise, country X isn't fighting one of those countries, it's fighting both of them at the same time, but they are devoting their full attention to X. If you are a player for country X, you will be outnumbered 3-2 wherever you fly, and to add insult to injury you and your outnumbered teammates will be flying FM2s against superior numbers of Spit 16s and ponies.
ENY does not work to balance sides. Encouraging people to switch from X to Y or Z doesn't accomplish anything if they keep on ganging X along with anyone else (and the ones who are too loyal to do that, probably won't be the ones to leave X).
In order to work as side balancing, ENY needs to account for WHICH of the two opponents each player in the air is fighting. That can be approximated pretty easily by looking at where they are on the map.
The only thing ENY forces people to do is make a decision.
According to the game designer, it is supposed to do more than that, it is supposed to work to balance the sides. It isn't doing that reliably.
To relate that directly to what you're saying, the decision it's forcing people to make is the wrong one. It forces them to decide which country to fight
for (and what limitations to accept as a result), but in a 3-way game numerical balance is actually decided by what country everyone is fighting
against, which is not the same thing at all.