There have been incidents, but there are probably less incidents than taxis or buses. In uber or lyft, both the driver and rider are known to uber, as well as the route the car takes, when the ride gets to the destination, etc. People who commit crimes during an uber ride are caught easily.
You can track the route on GPS. When we took Uber over home from the hospital after my husband had a heart attack, you could track our progression going home. It was kind of neat my daughter loved it!