@Kaarme , ahh yes, it's perfectly fine that you as an "educated" reader connected the dots.
But you must think of the characters themselves.
The smartest man of bunch would either be Benno or the Merchant Guild Leader. Both of whom, did not advise the church as an option for Myne.
This is likely not due to malice, but due to either ignorance (not connecting the dots that the church would be willing) or did not think it was possible.
After all, under normal circumstances, they only let nobles use the magic tools!
Now we bring it back to her family. If the smartest guys around didn't entertain the possibility, would the poor peasants with even less knowledge consider it?
Probably not!
About the church helping out one of their own.... Well, discrimnation is very real.
It's very likely only due to the present situation (post-war, lack of magic supplying nobles) that they'd consider a commoner to supply magic.