24x7 is hyperbole. No one literally wants to be there 24x7, but some people want to be at work more than others. If your argument is that no one can maintain any more than a 40 hour work week without burning out, I disagree.
So yes, even aware of burnout, I would still want to fill my company with people who want to work more than 40 hours a week.
This may be a twisted analogy, but I think of work in a way similar to how one properly cages a dog. Some people make cages a place of punishment for their dog; break a rule, be disruptive, and you enter the cage, which is far away from all happiness or socialization. It's a place for bad dogs. It makes the cage a hugely negative place for the dog, and causes all kinds of anxiety and trouble.
The solution? Make the cage an everyday and normal part of the dog's life. Put the cage in the middle of a high-traffic area, leave the door open so the dog can go rest in the cage when it's tired, make the cage a comfortable and happy place for the dog, and it becomes much easier to put the dog into the cage when the time calls for it (company, leaving the house, etc.).
Work should be thought of similarly. It can be your 9-5 cage, or it can be a place you come and go, a place to willingly spend free time, a social experience where you interact with cool and interesting people who you'd hang out with even if you didn't work with them. In both cases, you have to be there 9-5, but in the latter case, you actually want to be there, and it's not associated with huge Dilbertesque negatives.
So when someone talks about "I want people who want to be there 24x7", they're talking about having a cage that isn't for bad dogs, but a part of their everyday doggy life.