What does a subwoofer solve? That’s a good way to put it, ‘solve’.
The thing is, doing without subs is simply doing without the low register; it simply isn’t there, nothing bad added, so I can understand that some ask why use them, and I too did without them for a long time.
I chose subs for speed and accuracy, not boom boom, and went with the philosophy that says, it’s a stereo, so bring both sides up to spec, so to speak, to fulfill at least 20Hz - 20KHz: and more so, you can’t tell from which direction 18Hz is coming from, but one can sense from where the higher sounds emanate, where the subwoofer’s contribution syncs with the speakers, so two subs make the sync more accurate and thus the soundscape is more accurate.
Since none of my speakers go below 32Hz, a pair of subs brought the floor down to 18Hz.
What they ‘solved’: they contribute the content my system could not previously recreate; they enable the system to transmit more towards the total of the available information.
Adding two subs fundamentally transformed my sound: I’d been building the system for three years and all the care I’d put into it ‘bloomed’ into a higher perfection with them; I felt foolish that I hadn’t prioritized them earlier considering they were some time and work to hunt down, but didn’t cost much.
Before the pair, during the months when I had only one, it clearly helped, but never sounded ‘just right’; it sounded like half the promise of what two could do.