As I understand it, what's hard is determining whether that stationary object is directly in front, or off to the side. Cars are always passing stationary objects on the sides.
And what's worse with systems like Tesla's autopilot, you don't have very much 2D resolution.
That doesn't really change my answer. If an object is almost directly in front of you, you either fine-tune your turning to avoid it, or you stop.
There's no reason to ever ignore it.
As I understand it, Tesla autopilot can't distinguish objects on the sides (such as road signs) from objects directly in front. And it must ignore road signs etc. So it ends up ignoring all stationary objects.
You can't just slam the brakes on the highway. Just a question of time until you get rear ended.
There are other ways to stop than "apply full braking power until speed == 0".