The police cannot section someone in their own home. It is considered a place of safety and is not covered by section 136 of the
mental health act (which gives police that power.) Usually in situations where a person needs to be forcibly removed from their own home for mental health treatment, paramedics go through their own processes to take away capacity under 135.
In my experience, when it comes missing persons enquiries, one of the police's first tasks (aside from obviously looking for them) is always searching that persons home address. Even if that's not were they vanished from. A few reasons for this. One, more people than you think just end up back at home, and it's a big waste of resources to put up the helicopter when they're obliviously eating biscuits at their kitchen table. Two, for clues of where they have gone and what their intentions were. Did they leave a note? Take money? Pack a bag? Is there signs of a struggle? Did they have a heart attack behind the potting shed and need an ambulance? Etc etc etc. That information is needed as early as possible to direct search efforts effectively.
NBs husband was sent back home because he was needed there. Not only for his daughters, but to let officers in, find a picture of her, approve media releases, tell them if anything was missing or wrong in the house, to be a point of contact for anyone they know who might call him with information. He needed to be available because police needed his personal insight and contacts to direct the search efforts effectively. Better trained people were doing the searching.
Him running about shouting her name might have made him feel better but it would have hindered the search significantly. Staying put and drumming up leads was vital. He did exactly what was needed of him, even though it undoubtedly went against any partners natural instincts. IMO
Lastly a concern for welfare is just that. They were checking welfare because somebody had called the police with potentially dangerous or time critical concerns about someone in the household (hence calling police and not family/doctors etc)
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