So, you'd rather it did what it said in the manual, and actually run into the car in front even though it could manage to stop, you would rather it just ran into the car in front, just to prove your interpretation of the manual?
That's rather perverse logic.
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If you actually read the paragraph, as a paragraph, rather than picking individual sentence, or words out of context, it is talking about what AEB is 'Designed' to do. It's "Not designed to prevent a collision" [from the front or the rear]. [In terms of It's design] At best, it can minimize the impact of a frontal collision by attempting to reduce your driving speed.
So, it specifically states, its not DESIGNED to prevent a collision. (Be that a collision from the front, or in this context, neither from the rear). It doesn't say that is "SHALL NOT" prevent a collision, when it is possible. It says that it's purpose isn't to prevent the collision.
It then goes on to say "Minimize" the impact of a frontal collision, by 'Attempting' to reduce your driving speed. Minimizing the frontal collision to '0' impact, is surely successfully minimizing the impact.
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So, although it's not designed to avoid the collision (at the front, or the rear - or the side for that matter), that does NOT mean that it is obligated to have a collision if it is activated. That would be a particularly perverse reading.
The fact that a rear collision also occurred, is actually what the Warning particularly highlights as a likely outcome.
"Depending on Automatic Emergency Braking to avoid a collision can result in serious injury or death"
i.e. Don't rely on it to avoid a collision, because it's not designed to eliminate the possibility (prevent) a collision, and even it it manages
You may also want to read the whole paragraph on AEB, which gives more than just the highlights on page 28 (Page 113)
Particularly the paragraph saying
"Automatic Emergence Braking does not apply the brakes, or stops applying the brakes when:
You press and release the brake pedal
You accelerate hard
You turn the steering wheel sharply.
etc.etc.
"
So, as has been pointed out, the car actually DOES have the behavior you are complaining it doesn't. It's just that you need to learn how to operate the car fully.
If you want to steer around the obstacle, then just do it.
If you want to continue to move forward, release the brake.
If you want to accelerate, then go for it.
Your driving the car, drive it how you want.
Also, follow up with reading the Obstacle-Aware Acceleration, which is intentionally the next section.
So, if AEB gets you down to 10mph, and then you accelerate the last few feet if you so decide, OAA will then kick in and stop you hitting hard into the back of the car, might be a soft hit, or might hit the brakes right up close. so you don't hit at more than 10mph approx. It may even actually even avoid the collision, and allow you to close that gap.
Then, go on to read the "Limitations and inaccuracies" paragraph. This outlines exactly the sort of things you claim isn't documented.
You might find it beneficial to "RTFM"