> It is clearly beneficial to not send whole teams of people looking for weeks for your stolen wallet like they would for a missing person.

A massive miscalculation -- stolen wallets, cell phones etc are individually small-ticket items, but the criminals who make a living stealing them do hundreds per month and thousands per year. Taking the perpetrator of a thousand muggings or pickpocketings off the street is a job worth doing, possibly more so than chasing small time drug dealers or runaway teens.