I actually have a question...if Mew and Mewtwo are essentially banned online, does the same apply to the legendary birds? Because if one were to have them all on a team, even though their stats are overwhelming, they are all birds, so both thunder and ice would be advantageous to two separate birds...
The birds aren't banned, mainly because each of them actually has weaknesses. Zapdos is stuck to Electric and Flying attacks, so it can't harm Rock/Grounds. Articuno, although having a huge Special, lacks the movepool to back it up. Same problem with Moltres, but Molt's case is even worse.
Then, as you have already stated, they're birds, so weak to both Thunderbolt and Ice Beam/Blizzard.
~and you can't argue against me, because I'm a girl! GIRL POWER!~ Endgame