MoN is a position to which you get nominated to by the Amyrlin Seat. Its almost like you're number three in the Executive (though you have a very very specialized role, where you are paramount).

Egwene, newly elected by the Tower Hall, fully has the right to take on a new MoN. she may just have heaved a sigh of relief at finding a way to put in someone more competent without snubbing Tiana too much.

I frankly fail to see why a BA sister would encourage Novices who can Heal to learn. That seems counter productive to the extreme, with the LB coming.