Putting my phone into a lost mode resulted in them getting my primary phone number which then later was used in a feeble attempt to scam me over WhatsApp. Pretending to be Apple's support, they sent me a phishing link trying to extract the PIN number of the phone. Every number they used (from DNS registration one to the ones they used on WhatsApp) was stolen from someone else before and reused. Funnily, given the domain registration dates they have been preparing for carnival for quite some time. Police wouldn't move a finger (I had a similar experience in UK when I had a Macbook stolen in a central London restaurant).
While Find My might be a useful tool if you forgot something at your friend's place, I doubt the probability of successful retrieval of a stolen phone is high. It's fun to track on a map but unfortunately Find My doesn't even provide a history of locations (!) where the device appeared - it's only the last approximate address where the device has been seen. The return to risk ratio of dressing up as a batman and trying to retrieve the device yourself is not the best, especially if it has been stolen by a "professional".