It's more about making sure that everyone's personal belongings are safe. We would rather they either be with the right people, or be safely in storage. It's nice to think everyone can be trusted to leave each other's things alone after they go missing, but wouldn't you feel safer holding onto something that belongs to your friends than letting them sit in an empty room unaccounted for?
We don't know what will happen tomorrow. We may get 150 new people. If news of the disappearances reaches people outside the mountain, they may take advantage of it and attack. If our missing people return, then there's nothing stopping us from returning everything to them, but we've had large disappearances before.