Several problems & issues have been mentioned.
One that I didn't see addressed is the nature of the game. Unlike the in other games which use auto balancing features for all players, there is a war going on in the arena. And this war isn't over in a few minutes or an hour, it can take many days until the map is won. One big motivation for many players is to win this war. Or to prevent the other side winning it while they are on. You would take that away if everybody could just be switched to another team (or auto assigned at log in). Imagine fighting in a pitched battle for an airbase, and suddenly you're on the other side before you can win it. OR you fought for the team in the war, and shortly before it's finally won, you are suddenly on the other side.
Also, there is still a longer term strategic element to missions in AH, most notably the strats. I personally would feel very uncomfortable having successfully smashed some key installations in a daring 2 hour sortie and suddenly find myself on the side I bombed. There would be no point for me in such missions, which I enjoy quite a bit anymore, if I could not reap the 'rewards' of it afterwards.
I do switch teams, but it's always on a per map decision: When I first time log on a new map, I decide if I stay on this side, or if it's about time for a switch. But whatever my decision, I stay on that time for the whole remainder of this map.
Yes, some players already don't care about the war or the teams at all, but they are not in the majority. Note how few players are green on the roster despite the big perk incentive?
Ripping squads & teams apart like this would create quite an outrage, much more than the ENY complaints could ever do.
That's a fair critique and the reason I didn't address it is because the fact that there's a war going on isn't reflected in the arena half the time. The reality is wars are only being won because one faction is steamrolling another in the middle of the night. If I could hazard a guess, most players (who know about the strategic objectives) don't care because they realize whether they win or not depends more on which of the three teams ends up stacked that night.
As for longer strategic missions I don't think you'll ever get balanced just after landing one. If you do It'll just be really bad luck. Bomber pilots getting balanced doesn't make sense either because their sorties are so long chances are the balance is being called for while they're in flight or while they're AFK. The data is there to differentiate what pilots are doing most of the time, so an algorithm deciding who to balance can factor that in as well.
It's already been stated what can be done about squads and wingmen. Just don't balance them unless you can keep them together when you do balance them. Auto balance doesn't have to keep the team balance perfect, just within a certain margin. If the teams are mostly balanced in player count, then using ENY to make up the remaining difference should be fine. Honestly auto balance is probably what ENY needs to be better, Since the problems with ENY seem to arise when the teams are egregiously unbalanced.