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.