What does a subwoofer solve?

Thanks again for all of the input.  I'll stand down on the subs for now and investigate some alternative placement of the room components, especially speakers.

One example of what I mean when I say they amp is shy on bass is Max Richter's Blue Notebooks album.  Second song (On the Nature of Daylight) just after the 1:30 mark on the song there is a sustained series of deep notes that you feel as much as hear.  With the BHKs, this was very present and audible.  On the Luxman, it's there, but barely.  This example translates to various other music.

I ditched the BHKs due to quality issues.  Three sets and they couldn't send me a pair that worked as advertised, so I gave up.

One more thing: The front end is a Linn Klimax DSM Katalyst (I know I'm in the land of mostly Linn haters here, but I can live with that).  Output impedance is listed at 300 Ω.

If you mean,’" What potential problems can a sub-woofer solve with regard to sound?" I would say many. And I would say in my own system, when properly integrated they supplement the low frequencies and allow me to hear lower frequency sounds. They add and enhance those lower frequencies because the sub-woofers I had chosen are flexible and designed to do just that. They can add lower level detail and allow my speakers to simply produce the frequency range they are designed to reproduce. I also think the allow my amplifier to work easier. in the end it’s a matter of your flavor of equipment and sound. Sub-woofers are just another way to get quality sound. But not always the best way. BTW even full range speaker systems have been known to benefit from quality sub-woofers. IMHO

If you don’t have at least 1 - 2 subwoofers you are missing a lot of low frequency energy that you didn’t even know was present 

fiesta75,

"If you don’t have at least 1 - 2 subwoofers you are missing a lot of low frequency energy that you didn’t even know was present ". There are no absolutes in audio. Not too long ago I was a big proponent of using dual subwoofers, not just for bass, but I experienced improvements across the audio spectrum. I recently changed amps and in my system/room I prefer  my system with the new amplifiers, minus the subwoofers over my system with the old amp and dual subwoofers. Based on my experience, I may never own subwoofers again for 2-channel.