Like honeylou, my children have a double barrelled surname... because I wasn't going to be written out of the family's history, simply by the fact that I'm female.
My daughter (21) uses both surnames and says that it helps her name to stand out to her tutors at university/will be helpful if she goes on to work in the industry she's studying. She also says (because like the OP I have wondered the same thing about where it all ends...) that if she gets married/has children, then she'll keep the first part of her surname and double barrel it with the husband/father's surname (or, I guess, the first part of his double barrelled name...!). She's actually given this independent thought and it seems a very sensible attitude - although her father might be a bit upset about him being written out of her family history, we'll cross that bridge if we ever get to it!
My son (12) refuses point blank to use his full surname and dropped his father's half - by his own choice - when he started school. He says that he simply doesn't like the sound of his father's surname, but likes mine. Which we can't/don't/won't argue with.
Whatever surname a child has... it's their name and they have the right to do with it whatever they choose. If Miss Goring-Smith-Baring-Jones wants to marry Mr/Ms Fortingly-Askew-Smyth-Montague, and double barrel their names, then so be it. It's their choice. But any children are more likely to have the first surnames double-barrelled (so they'd be Master/Miss Goring-Fortingly, I guess...) in my experience.
And for the poster whose friend claimed to "know" that any children registering at her school were those of unmarried parents... how snobby is your friend?! And does she really think that all of the upper-class members of society are the result of unmarried parents, stretching all the way back to the 11th century?! My grandmother had a double-barrelled surname (well, actually, she had about five surnames all told at birth) and she certainly was not illegitimate! Nor were her parents, or her grandparents, or so on.