Traditional radar is bad at spotting stationary or slow moving objects, and to avoid false positives at every traffic sign or other stationary object above or next to the road, any radar-based object detection has to be tuned conservatively or the car would be flipping out all the time.
That’s why other companies use lidar, which is much better at object detection, but has its own problems (like fog or heavy rain, for example)
Stationary objects are very detectable with radar as they have relative motion to a moving vehicle. Also objects with no relative motion are only tricky for CW doppler radar.
The issue is mostly your last point. The radar sensors used have low resolution and would have trouble distinguishing a turning semi from an overhead sign.
That’s why other companies use lidar, which is much better at object detection, but has its own problems (like fog or heavy rain, for example)