Both my teenaged ds and dd are at boarding school. Their choice. They applied to both boarding and day schools and chose to board because the range of activities and the time in which to do them were so much greater in the boarding schools.
So far, they are thriving. We've been fortunate that our children each seem to have found a school that suits them, both with strong pastoral care. We are not millionaires and we did not enter into into this lightly; when we did, many of the sensible points that JanetBrown has made above were very much on our minds.
I appreciate this is just my personal experience and it's not for every parent/child - I just hate to see boarding school written off as being tantamount to neglect/abuse when our dc's experience of it is such a positive one. Also, when we see the housemasters, tutors and other staff in our dc's schools going to such lengths to ensure that it is positive.
There are ups and downs for my dc, of course, as there would be at any school but I do still feel as though I share in those ups and downs as I see them very regularly - ridiculously long holidays, plenty of weekends home (when they're not too busy to want to come!) and I go to nearly all of their matches, etc (although as JanetBrown says these are not quality 'bonding' occasions - I go to support them as I would if they were at day school - they are valuable all the same) and my dd calls every day (believe me, I still hear ALL of the "every day grumbles, grouses..daft conversations" and the minor stuff). Ds calls when he's particularly up or particularly down but is always happy to chat when I call him in between. It's much easier to pick up on the nuances of emotions on the phone than you might think - if they're down, I know it, can talk them though it - ask their housemaster/mistress/matron/best friend to look in on them and even if I can't hug them there and then, they know that I can get to school within the hour if needed...I admit we all miss the hugs but as Wankstainwasher (hilarious name! Presumably they save it up for the holidays?!) said, there are plenty of these when they do come home and time at home is all the more valued for being precious (and homework free!).
I love picking up both from school for weekends and breaks - a friend who also has boarding dc described the feeling as like going to meet a new boyfriend with whom you're completely smitten - it's just like that. I love the smart, chatty, sociable confidence that seems to grow and grow in them every term. I love having them around but I also love that when they are at school they are free to develop into these wonderfully independent beings - to make their own choices, good or bad: spend every free minute pursuing their interests, with their friends, playing sport, in the art school, smoking behind the bushes - whatever - without me hovering over them, yet knowing my feelings about all of the above and that I'm always a text away and can drop everything and get to them if ever needed. It certainly feels very healthy for our family and I feel no less of a mother for my children being away. I certainly don't think about them, plan for them or worry about them any less.
For their part, yes, there will be an element of coping and managing beyond that required in a day school - but I think that as teenagers this is no bad thing if underpinning this they have trust in and feel supported by their parents and school staff. I believe that social awareness that can be gained in boarding is invaluable - learning when you need your personal space and how to find it; appreciating when others need theirs; learning how to seek support from friends and knowing how to give it. Of course this comes at the cost of missing out on being in a more nurturing, forgiving family environment but I like to think that my dc have the benefit (and the flip sides) of both.
It is certainly not a decision not to be taken on a Malory Towers fuelled whim but we have no regrets. I wouldn't write it off OP!