The fantasized "24/7" relationship that involves total slavery and submission is, I think, a fantasy. But that doesn't mean that 24/7 relationships don't exist in one form or another. For some people submission or domination is just a natural expression of their way of relating to those close to them, and I think for many people - myself included - D/s is not just a sexual reality.
My submissive, for example, is about as selfless and helpful a person as I've ever met. She has so little regard for her own pleasure, and her own desires, that she tends to get swept up into her work, and into what others tell her to do. She is, in essence, entirely submissive - not just sexually, but in most everything she does - and our D/s relationship arose more out of a non-sexual need than a sexual one. Without having a dominant to serve, who can look after her occasional need to be selfish, my submissive would tend to allow employers to take advantage of her willingness to work too hard, to take on too many projects at once, and to, ultimately, bury herself in service.
That is not to say that we have a one-way communication in our relationship, but rather that it is my responsibility to keep her from her own good intentions, while she helps to keep me focused and motivated in what I do because of the value of the gift she has given me (that is, the gift of her service). We do engage in a kind of sexual roleplay, with ropes and clamps and so on, but that is just an extension - or maybe an overexaggeration - of our day-to-day interaction.
Perhaps some die-hard would say that, because we communicate, my submissive and I do not have a true 24/7 relationship, and that because she has a safeword, she hasn't really turned over control to me, but I beg to differ. I think it's really a matter of personality: most people, I think, have dominant and/or submissive tendencies (I believe almost every relationship - even vanilla ones - have a degree of D/s, whether acknowledged or not), but some people are too submissive or too dominant to just "play" at it. I agree with Daumon that no one lives in true 24/7 sexual slavery, but I do think some relationships have a permanent power-structure.
I think it is important to play before turning a relationship into anything permanent. My submissive and I were together for years before we determined that we were involved in something of a 24/7 D/s situation, but the only thing that really changed with that realization was some of the language we used to describe our relationship. Fundamentally, our relationship had always been D/s without us even acknowledging it, because that was who she was, and who I was. This fictionalized fantasy where submissive but not aware pain-slut meets dark and mysterious dom who turns her into a sex-slave is grossly overblown, much as it appeals to one's sense of fantasy. The reality - for me at least - was much more commonplace, and not all that different than a normal relationship (that's not to say that "commonplace" = "boring").
A final note: in a real 24/7 relationship, the dominant serves the submissive as much as - if not more than - the submissive serves the dominant. Granted, the kind of service each gives is very different, but there has to be balance. Otherwise the relationship simply cannot and will not last.