In practice it does leave a bit more following distance than most human drivers, but your worry of constantly getting cut off until you come to a stop in the road is not a real thing. This is partly because the car modifies the set following distance based on speed, so that the same setting is much closer at e.g. 5 mph than at 60.
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.