Why the obsession with the lowest octave

Good point that even instruments do not have a single sound. It is a function of the environment played in (ie the venue) and the sensors used to detect the sound (ie your ears, microphones, etc) that create the variations.

Facts like these are the reason why while can appreciate the value of a good venue, I always have to chuckle when it is suggested the room you listen in has to be effectively neutralized completely to get the correct sound.

The fact is the room in which the music is recorded and the room in which the music is played are both factors in the resulting sound in a home system, as much so and often even more so than the system played on.

Practically, the goal should be to optimize the resulting sound to sound good to you, not to achieve some perceived standard of perfection that does not even exist and cannot practically be achieved at any cost.

That thinking is good for the vendor though! It keeps everybody chasing the carrot and draining their funds indefinitely to achieve an impossible goal.

I've found it interesting that while the OP ask about the "lowest octave", which would commonly be defined as 20-40 Hz, so many replies have commented on bass in general or if specific, reproduction above 40 Hz.

But for the general value of a decent subwoofer (or bass extension), I had a learning experience similar to Ecruz. Many years ago I visited a well-respected dealer for a sub-woofer demo. The main speakers he chose were Spendor BC-1s (that may hint how long ago this happened) with an excellent mid-range reputation but known for low frequency limitations. But to my surprise, for the music demo he used a solo violin. Even with such a limited low frequency range of the instrument, it was very obvious when he switched the sub system in and out. That forever sold me on the value of extended bass (again in general, I'm not identifying a specific frequency) for a fuller musical experience.

Why the bottom octave?

Because it sounds so right, when done right.

If it was there when the music was recorded, why not have it there in your room when it's played back? The hard part is doing it right.

If you understand the physics of sound production with musical instruments you might understand better the "obsession" for the lowest octaves. Although one may not be able to hear a very low frequency bass tone the fact that the speaker can produce low frequencies and may be vibrating at a low frequency sets up the mid range and high frequencies within the harmonic series to produce a more resonant quality. Musicians choose instruments with this quality and tune their instruments to tap into this harmonic structure so the instrument sounds better. These vibrating harmonics, even if they are too low to hear, bring out upper harmonics to add color to the quality within the speaker and accoustically in the room air. Some musical instruments are better than others by just they way they are made and I imagine speakers are the same, some good, some not so much. Walk over to a piano (any piano but a grand piano demonstrates better) and push down slowly on a middle C so the hammer doesn't strike but is off the string and hold it down. Then, while continuing to hold down the middle C strike a C in one of the real low registers for 1 second and release to dampen that note. The middle C will be vibrating when you release the low note and it was never struck due to resonating harmonics from the lower portion of the harmonic series. Bottom line is a speaker that has a great low frequency quality will make the entire spectrum and system sound better.