Perhaps you've seen The Big Lebowski. "Leads? Leads?"

The odds of the SFPD "investigating" a mere wallet theft are even lower than the Malibu PD trying to figure out who stole Jeff Bridges' car.

For one thing, after Prop 47, stealing anything under $950 is a misdemeanor. A misdemeanor is basically a traffic ticket for anyone already involved with the criminal justice system. Misdemeanors basically do not result in any kind of custodial sentence in CA today.

Only a reporter could get them to care at all. ("Journalist privilege" is real.) Even then, they can only care so much.