If AH was truly anonymous there wouldn't be any reason not to change countries. In fact in the beginning I tried to stay on the smallest side just for that reason. The problem arises when you start to have friends online, join squads etc. Then it starts to suck to end up fighting a friend after a side switch.
I once ended up against my old squad 7 to 2 and I downed 3 of them before escaping. Needless to say some took it with a laugh, some got upset, some very upset.
To put it bluntly, it was not fun and made me regret switching sides. Same kind of problem is with arena caps, most often than not some member of the squad gets locked out from the arena the rest are already in and typically has to quit for the night. No point flying 30 person arena with all the friends just behind an invisible wall.
The problem of the game is that it includes social elements. Both social and anti-social.