I kind of get what you are saying Evil but I think your slightly sneery
"As a mother, I deal with issues like this by talking to my children myself, not by contacting their teacher and expecting her to deal with it."
suggest that either you are not understanding me or are just being obtuse.
I will go with us misunderstanding each other
I haven't suggested that the teacher be asked to sort it out. Nor have I suggested that I wouldn't discuss it with my child before mentioning it to the teacher.
I said that I would talk to the teacher about my child being the only one of a whole class of girls left from an invitation as a means of checking whether this was a bigger issue or just a friendship group thing
The latter is not a problem. The former may be. But if parent and teacher are not speaking about it then a bigger issue may be missed.
Problems are not neat little extracts from a daytime drama - they can be hard to spot and may consist of a few red flags which don't imediately get spotted
The OP didn't suggest it was bullying but the whole point of her op is that her DD was left out. And that could be a whole host of issues - bullying was just one suggestion.
So whilst I know on AIBU we could enjoy 'sensible parents deal with themselves vs wimpy ponces bothering busy teachers' I think that as a parent saying
'look DD isn't invited to this. Can you just tell me if there are any reasons why I should be concerned that there is an underlying issue. Are you aware of anything? No? Great - bye'
Or maybe even 'are you aware of anything going on'
'well actually .....'
It isn'tthat crushingly burdensome for tecaher is it? Nor an abdication of parenting.