I agree that you threaten when unarmed, and that you can trip as AoO both when armed or unarmed (you're tripping with legs I guess).
But if you have a ranged weapon or reach weapon and therefore you don't threaten the adjacent squares, why can't you AoO-trip someone who's drinking a potion close to you? Or simply keep the bow/javelin/reachweapon with the left hand and strike with a fist as AoO?
Is it just a matter of choosing: this round I'm taking 2WF penalties so that I can make AoOs, next round I don't and won't be able to do AoOs? Can you actually take 2WF penalties with a bow?
BTW, just to be sure, does it say somewhere that a reach weapon threatens 10ft away but not 5ft away, or does it only say you can strike 10ft away but not 5ft away without mentioning threatening?