What does a subwoofer solve?

This has probably already been said but a sub, or subs, can solve the problem of placement.  The best location for bass is unlikely to be the bast place for the rest of the spectrum. 

In my opinion the ideal situation is to have large speakers with big woofers that provide a lot of punch and upper bass energy, but that roll off the deep bass gradually starting around 80hz.  Speakers that have deep bass extension flat to 30hz almost always have negative room interactions.  These would be greatly reduced if they had a -3db point at 60hz and typical sealed box roll off.  The deep bass is ideally filled in by multiple subs placed where they provide the most even response.  Taking deep bass duty away from the main speakers and amps reduces distortion and the amount of power required.

Are you using a power conditioner? Sorry didn’t read every post. I own some PS Audio monos and it seems they prefer power conditioners to perform there best in my system. Cleaner bigger bass. I run passive conditioners. Some of my other solid state and tube amps the conditioners take away the bass and full presentation. With those amps I  go straight in the wall. The difference is not subtle.

I tried subs long ago, didn’t know how to dial it in so had to let them go, since then haven’t been a fan of subs. Maybe if I knew how to set them up I would have a pair now.

For those that have tried subwoofers in their systems and didn't like them, the usual reason for this is improper placement and integration.  They can take quite a while to set up properly and incremental changes can yield great results but could also make a mess of things.  Any easy was to visualize what is happening in the setup is to use a laptop and REW, Room EQ Wizard.  It's been around for many years and is quite a helpful tool in subwoofer setup. 

Keep in mind that without knowing how your particular room reacts with bass and your seating position, you could be chasing your tail for weeks or longer growing more and more frustrated with the setup experience.  In our last house, I spent a whole weekend setting up 2 subs in our family room, running dozens and dozens of sweeps in REW, each time altering settings in the preamp or the phase settings on the subwoofers, or the physical locations of the subs, volume settings, etc., etc. to get it right.  But once I had that done, with the subs properly married to the system and the room, it was fantastic.  You just can't plop a subwoofer or subwoofers down any old place in your room and expect good results.  Patience is key to unlocking what they can do for you.