Unlike the rest of your post, I disagree with this statement. Ideally any drive unit will have flattish and smooth response above and below its passband. A subwoofer should be flat smooth and clean at least an octave above its intended range. I like to use subwoofers higher than standard to gain headroom and extend the response smoothing benefits of spatial distribution. That means flattish and smooth FR out to 300+ Hz.
Also, bass management should be centralized, not ad hoc cast out to individual components. Decentralization just makes it harder to optimize the system response. If a subwoofer amp has a high pass, it must be defeatable for the subwoofer to be generally usable.
I consider this subwoofer and the one Erin measured borderline unusable due to the limited bandwidth imposed by very poor design choices.