They're really all about their Aes Sedai club, rather than channeling or anything else. Anyone who can't be in the club is out. Once they decide you can't become a sister, you're gone as soon as they've taught you enough that kicking you out isn't negligent homicide. They really and truly seem to think that being Aes Sedai is a bigger deal than channeling, what with the comment that they seem to think women banished from the Tower would let their ability atrophy, that they would not care about channeling if they couldn't do it in a shawl. Another example would be Else Grinwell, who was sent away at a time when the Amyrlin was aware that Tarmon Gaidon was coming really soon. It wasn't a strength issue, as Siuan implies, if not states outright, IIRC, that she could have made the shawl, but they decided on less than a year's acquaintance that she'd never ever overcome her interest in men. So a perfectly strong channeler is disposed of, because only Aes Sedai and the shawl are real to them. Egwene is affected by this too, with her rushing girls she herself does not believe are worthy through the ranks in preparation for Tarmon Gaidon (though she refuses to force them), in the interests of needing more sisters, as if Accepted and novices can't contribute without a shawl on their shoulders.