This could easily be solved if everyone called the police when they found a lost child and let them sort it out. Also any doctor could have "break through" access along with the hospital they are at has it as well.
I’m not sure that’s an efficient solution at all. If a kid gets hurt/lost in my neighborhood, I’d much rather be able to call their parents than add an entire extra step of calling the police and having the police call the parents.
Calling 911 could generate a misdemeanor or felony charge (neglect or abuse) for the parents. Use it if you believe the situation warrants it, but at least in the US its better to avoid involving the police just due to social liability.
Given the current state of phone network security, "You can trust I'm a real doctor because your phone rang when I called you" doesn't seem like a good solution.