Dear Dr. Cornelius,
I think you have excellent insight into the nature of the two Beastmasters. Given the current card pool, their abilities would indeed make sense to be switched. However, should they ever release a Quick Attack Ranged Weapon, such as they have hinted at, then the Johktari's Fast trait will make her an awe inspiring skirmisher with a bow.
Regarding your currently stated tactics, I suspect your meta just hasn't caught on to a few good counter strategies. Obviously, rushing your mage would make the bow useless and should be a top priority anyways since killing the Mage is the game winning condition. Falcons won't even hinder them from getting to your mage normally. Having a swarm present within the meta, I would also expect AoE spells, like [mwcard=MW1A12]Ring of Fire[/mwcard], which could potentially kill all of your birds in a single spell cast. [mwcard=MW1J16]Mordok's Obelisk[/mwcard] and [mwcard=MW1J21]Suppression Orb[/mwcard] also are likely to become common. There are good reasons why neither swarms nor bows are common practice currently, and I suspect your meta will eventually make you feel these reasons as well.