It's not just the fees; school trips, music lessons, kit, uniform all the extras that need to be factored in.
If your dd is keen why not go to the open day and give her the choice?
Some dc especially if they 'shine' and are gregarious do really well at boarding school; and there are often scholarships to help for music, particular sports etc.
There is also a sizeable number of dc who get sent there whose parents are abroad/work long, irregular hours and/or have split up with new partners/new families/parents on the 'social scene' so have hectic social lives or live lives not suited to or want the day to day routine of childcare.
Very good friends of mine sent their dds due to personality clashes with them, or their new partner or because they did not want to deal with the teenage years/'histrionics'/backchat and preferred the houseparents to deal with it all.
Statistically a large proportion of CEOs and other very successful, driven people (more than the general population) are sociopaths or have sociopathic tendencies and while this is not necessariy a bad thing (this does not equate to murderers btw!) it means that there will be a sizeable number at boarding schools.
Before you all leap at me I will say I think a boarding school is a perfect place for such children, but it does mean that any child at the receiving end/victim of this type of personality there would be no escape.
So if your dd was shy, retiring, lacking in self esteem/emotionally fragile and not very good at sports/music etc then she might find it very difficult.
On the other hand, my sister taught at a highly academic/competive girl's boarding school where one girl did not want to board, was crying, and grabbed hold of the metal jaguar on her mum's car bonnet while her mum was driving off down the drive and trying to shake her off.
She managed to dislodge her daughter and left her on a crumpled heap on the gravel and drive back to London but thank god the staff were wonderful and so for her the best place was definitely at boarding school where the staff actually cared.
Other times (so frequent my sister ended up leaving) when a girl was really upset and just wanted her mum/ wanted to go home and all inschool options were exhausted my sister would ring the mother and the mother would be cross and say that's what I pay the school for! Or who can I pay/what therapist can I get? When all the girl realy wanted was a cuddle from her mum!!
It's so common it's normal in such schools unfortunately. But yes, state schools have their faults too but the whole point of weaning your child off emotionally depending on you is the biggest difference.
Boarding school dc learn to depend on their peers for day to day emotional support and tend to view their parents as cashcows! So basically come to their parents not for emotional support but when they want money/material things.
Children who do not get emotional support at home/whose parents are too busy/have a dysfunctional relationship with them are much better off at boarding school.