I do think people who are root and branch opposed to boarding school are doing a great injustice to the fantastic staff, who become additional 'important adults' in the pupils' lives. My children who are no longer at school are still very much in touch with their housemasters/mistresses. They certainly don't regard these as people who brutalised or traumatised them. The friends they made at school are friends for life. There was bullying at all of their schools - but there was also really vile bullying at the girls' day school one of my DC attended for a while.
I think people who don't currently have children at boarding schools have a very one-dimensional view of it. I personally wouldn't have sent any of my DC to Radley, say, for the sole reason that it's where "all the men in my family go". But if I'd thought Radley was the best fit for one of my DC, that's what I would have chosen (I didn't, as it happens). One school (Gordonstoun) was ruled out as my ex husband went there and hated it, though I am sure that's different now, too.
So part of it is, as with any school, choosing a school that you think will suit the individual young person. Another part of it is making it clear to them that if they give it a go and don't like it, they don't have to stay. Another part of it is making it clear that they don't have to board at all if they don't want to. One of my DC didn't board until the sixth form (and absolutely loved it then). I think we have moved on from the days when young children were wrenched away from the nest willy-nilly.
In terms of closeness, I haven't observed any difference between the parent/child relationships of families whose children board and those whose children attend day schools. If you are a warm, loving, engaged, talkative, emotionally intelligent family, then boarding/day makes no discernible difference. My dad went to boarding school in the 60s and is a lovely, kind, funny, well balanced man - far from the repressed, cold, emotionally illiterate cliche.
However, I very strongly believe that this kind of bonding happens above all in the early years - hence I was a SAHM. I was particularly keen for them not to go to nursery - I suspect one reason that the research into nurseries on child development is not more widely publicised is that it doesn't fit with the government agenda of promoting mass childcare to get as many women into work as possible. I wouldn't have sent any of my DC to boarding school at 8, either (although I think there are can be very good reasons to do this - choir schools). Once you've got that secure bond, though, sending an enthusiastic teenager to a school which suits them and enables them to do all the things they want to do can not really be a bad thing.