Here’s an October 11, 2018 report from Austin, TX on their Dockless Mobility Program, http://www.austintexas.gov/edims/document.cfm?id=307564 
Some interesting statistics from April - October:

Number of devices in service
Scooters: 3,750
Bicycles: 1,200

Miles ridden
Scooters: 1,190,900 
Bicycles: 85,000

Number of crashes
Scooters: 37
Bicycles: 81

Computation: bicycles had 30 times higher crash rate than scooters.

None of the scooter crashes was fatal; 1 was life threatening; 16 had “significant signs and symptoms” and 14 were non-life threatening.

During the same time, Austin had 
Pedestrians: 14 fatalities; 112 injuries
Motorcyclists: 5 fatalities; 128 injuries
Motor vehicles; 10 fatalities, 2,336 injuries

At least in Austin, scooters look like a pretty safe way to get around.

Frank