Earlier quoted context omitted.
On my Honda if a car merges in front of me and is accelerating, it maintains its speed presumably on the assumption that the separation will continue to increase. If a car merges in front and is slower than me, i.e. separation is decreasing, it will brake in an attempt to maintain the set following distance. In practice it does leave a bit more following distance than most human drivers, but your worry of constantly…
OK, it's good to know that it won't stop. But if it slows automatically it will still result in the same thing. All the other drivers just continue to cut you off indefinitely.
Interpreting your original comment in that context: AEB only kicks in at a point where maximum braking will result in you barely not hitting something in front of you, or maybe even hitting it at a low speed. Modern cars can stop very fast indeed with maximum braking so in practice this threshold is never crossed under normal driving conditions unless the software returns a false positive. It's not about maintaining a safe following distance—it's about stopping the car at the extreme edge of the safety envelope, beyond which no manual or automatic intervention could prevent a violent crash.
False positives do happen but I think they are very rare or practically nonexistent in good implementations. I've never had it happen with my Honda.