Would it be respected in a way that NO public statement and flooood of news about Andrew Gosden being alive and contacting police? Without dwelling WHY he stayed away, WHY he doesnt want to get in touch with his family, without baseless insinuation that his family must be horrible (while the reason of his disappearance might be not related to them doing anything wrong)? Without his family's further public pleas to get in touch with them?It's unlikely that he's alive otherwise he would've made contact by now or at least told the police he's fine and doesn't want to be in contact with anyone.
There was a woman who ran away from her family after abusive husband attacked her and threatened to kill her. She reported it, he kept acting same way (allegedly) so she ran away. His actions were enough for cops to consider him a suspect in her murder as they knew he was abusive and aggressive. Long decades later she got located, her current pics (with a source listed as cop's archive) ended up all over the media, she got doxed and portrayed as evil maniac who ruined her ex husbands life by framing him into her murder (by disappearing). Some people were understanding, most were pretty aggressive with their comments, family were posting horrific insults about her.
It should be simple: you notify cops, explain or nor explain your reasoning and investigation ends, nobody wastes money on searching upon making sure youre safe but it doesnt work like that. Or maybe it does for some people, but available examples suggest extreme public scrutiny (to the very least).