Your argument works equally well against you. Most people agree the search is justified if it's a missing girl, therefore it should also be justified for any tr

Your argument works equally well against you. Most people agree the search is justified if it's a missing girl, therefore it should also be justified for any trivial crime as well. But obviously there is a difference between trivial crimes and kidnappings. Inconveniencing a few people to save a life is acceptable. The expected utility is positive. It likely is not for more trivial crimes.