Who needs to trust them, if you have the means to fight them? The Aes Sedai can get away with anything they want regardless of what Oaths they swear. With their monopoly on the One Power, who can stop their elite warriors with enhanced abilities from killing anyone they want dead? And if someone dares to resist the assault of a warder and defends himself, the sister is freed of all restraint by the Oath to kill her target. The Oath against lying does not make them more honest, it only protects them from the consequences of dishonesty - disbelief. No one can ignore or refute an Aes Sedai who wants to make people believe the truth, no matter how severely she has abused people's trust in the past. As for the weapon Oaths, they protects the Tower more than anyone else, because it effectively prevents the Aes Sedai from giving genuine aid to their allies, and allowing them to claim credit for anything they want. Side A has an Aes Sedai advisor, Side B has an Aes Sedai lying low in their camp in secret. Side A wins, the Aes Sedai takes all the credit for her timely advice, and implies the sister found in Side B's tent was actually working with her to hand the victory to Side A. 'No, we can't give you details! Aes Sedai do not use the Power as a weapon, so we must work subtly behind the scenes, and such methods must remain secret.' Or if Side B wins, it HAS to be through the machinations of their secret Aes Sedai counselor. How else could they have defeated Side A which had an Aes Sedai openly working with them? See above re: the methods used to aid Side B.
The final Oath, against making weapons, is also for the benefit of the Tower in another way - it prevents any sister from making anything that would give normal people a way to oppose the Tower, such as happened in Seanchan.

Don't go looking at the Oaths like they protect the world from dangerous channelers. The only real protection is other channelers who are ready to take down a potentially abusive channeler to gain credit or advantages over the bad channeler's organization. Channeler running amuck? Have the local magistrate whistle up a detachment from the National Channeler Corps to deal with the problem, or hire a channeler from Channeling Associates LLC. to protect your town from him. Presumably people could also hire out defenses from such a source. Channelers could weave alarm wards around homes, or ward farms against vermin or weeds, or fire-retardant wards or any number of things. When there is profit involved, there is no limit to what human ingenuity can provide. The more diverse the channeling entities are, the less chance there is for any one to oppress people. And when the channelers are not a monolithic organization with oppressive clout, they can't use their influence to punish ordinary people who manage to defy their edicts with an arrow in the back or a knife in the dark.