Yes Seta asked later to be taught as well, I don't think we ever learned her motivations for doing so though. I don't rememeber any POV from her about missing saidar. Possible though I guess if you can find the passage.
Perhaps something to do with coming to respect the Aes Sedai, being afraid...
You mean Bethamin and Seta right?
I'm pretty sure you're imagining the whole missing the One Power business.
As far as I remember Bethamin started to channel when she was under the impression she was in danger from the Aes Sedai, and even then tried to say they didn't want to learn,
Let me...