Min used as messenger to Amyrlin

The premise is that a even a king may not be allowed access to the Amyrlin, but any poor woman would be allowed...

why?

i just accept these things when I read them, that’s their society, but there is no reason to prefer women over men. Given Min’s excuse later, she should have been spoken to kindly by any aes sedai, and then sent to wash dishes if she persisted, not swept into the Amyrlin’s office.