This is a known issue, and there are videos online where it has caused wrecks. Despite such balderdash we repeatedly see posted here, Tesla's cruise control (TACC) is not to be limited to controlled access roads. It can be set as low as 18MPH, and controlled access roads have minimum speeds of 40MPH. Tesla does state that it is not for use on city streets where traffic conditions are constantly changing, but there are a great many roads where people can turn left in front of you. For example, the difference between a freeway and a highway that a freeway is controlled access, and highways are not. Tesla's owners manual SPECIFICALLY STATES that it is "mainly to be used on dry, straight roads, such as freeways and HIGHWAYS."
TN state law requires 2 seconds travelling distance between cars. NHTSA uses 1.3 seconds as a reaction time. It doens't take long for a group of cars, even those actually following the 2 seconds, to overcome that differnce when Teslas TACC brake checks. People typically drive about 30' (the stripes are 10 feet long) around cities in my experience (Lexington, Atlanta, Nashville, Knoxville, Macon, Greensboro, Raleigh since I've had my Tesla),. 70MPH is 100ft/sec. So yeah, do the math.
That said, the car has gotten better at it as I've driven more, but I also anticipate when it happens, and depsressing teh throttle slightly will prevent that. I still wish conventional cruise control were possible on these cars.